A Hidden Assumptions in Bell's Theorem?

[vanhees71]

There is no entanglement between 1&4 in the full ensemble, not even after the BSM, so if there are entangled subensembles after the BSM, they must have been there before the BSM. It's very easy to perform the decomposition. If you have an ensemble of coinflips, then 50% of them will be heads and 50% will be tails. You can just sort them into two subensembles that are no longer uniformly distributed. Sorting the uniformly distributed ensemble of the 1&4 system into buckets that match the statistics of the entangled Bell states is only insignificantly harder.

It's even shown in the very short and to-the-point PRL by Zeilinger et al:

https://web.physics.ucsb.edu/~quopt/swap.pdf

It's a nice exercise with manipulations in the bra-ket formulation, suitable for a problem in the QM1 lecture!

 

[martinbn]

@DrChinese Let me ask you some direct questions.

1. In which sense do you use the term non-locality? Is it meant as violations of Bell's inequality or something else. If it is only in the sense of violations of Bell's inequalities, then why do you need to talk about entanglement swapping? The violations can be demonstrated without swapping. If it is something else, can you clarify what it is? And do you claim that your references (Zeilinger, Weinberg and so on) use it also that way?2. Consider a pair of two systems A and B in an entangled state. Then there are two standard facts, that have been mentioned and can be found in the literature. The density matrix of B has all the information about the statistics of the possible outcomes of measurements on B. Any measurement on A doesn't change the density matrix of B. The question is: do you dispute any of this? If yes, can you explain why. If not, then why do you say that the statement "Measurement on A does have an effect on B. Or the cause of a result at B is the measurement on A." is interpretation independent? Actually you say it is a proven fact.

 

[Simple question]

The quoted scientist use the term "non-locality" to refer to the presence of Bell-violating correlations, nothing more.

As does DrChinese. All this is a-causal, only you are invoking "causation" and using prefered "interpretation". As shown in your next sentence:

You use it in a much stronger way, implying that Bell-violating correlations somehow require the existence of non-local cause-and-effect relationships.

Strikeout mine. This is your mistake only.

I'm saying there is no evidence for a non-local cause-and-effect relationship. Correlation doesn't imply causation.

Correct. But if we stick to experimental facts, the SMB at 2&3 is "spooklily" sniffing those correlation about a big chunk of a space-like region (1&4 detection's events). That is why anyone can use "non-local" in a perfectly simple and SR compliant way.

The Bell state measurement does not affect the 1&4 pair.

That's your way to "interpret" things. I think everybody is silent on this, because there is simply no standard understanding on how nature does this (an stunningly, in a-causal way). Nor does exist any theory that can explain this using locality, as proved by Bells (if those assumptions are right)

The full ensemble of 1&4 is not entangled.

Correct. So why are they running those experiments ?

The subensembles are entangled, but it is a well understood statistical fallacy to conclude that there is a cause-and-effect relationship because of the conditioning on an effect.

And there is another fallacy that pretend there is a theory that can locally pick-up a a sub-ensemble. Because one can also play that game with pairs of socks, and I don't think quantum theory applies to socks.

Again, there is no evidence for this. This is completely interpretation dependent and there is currently no known way to test it even in principle.

This is wrong. In principle you can use entanglement swapping, and realize it by experiment. And if you choose to interpret it as 2&3 does nothing., you are simply wrong.
2&3 pick up a correct sub-ensemble about 1&4, and in a plain an simple non-local way.

So if you are happy with the "shut up and calculate", then compute "non-entangled".

Meanwhile people happy with quantum mechanics and various mirror lazer and polarizer, will build such intricate (and delicate) appliance, to protect 1&4 to be tempered with.
This means something physically happening at 2&3 will add to something physically happening at 1&4 (both space-like separated, mind you)
All this in the lab, not in "interpretation space"

 

[vanhees71]

@DrChinese Let me ask you some direct questions.

1. In which sense do you use the term non-locality? Is it meant as violations of Bell's inequality or something else. If it is only in the sense of violations of Bell's inequalities, then why do you need to talk about entanglement swapping? The violations can be demonstrated without swapping. If it is something else, can you clarify what it is? And do you claim that your references (Zeilinger, Weinberg and so on) use it also that way?

Let's look at Weinberg. In his textbook on quantum mechanics (2nd edition) he defines

As you see it's a very weak form of "locality", but it's in accord with locality as understood in the connection of relativistic QFT. Everything else were very schizophrenic, because Weinberg is the one who used microcausality for decades to establish the foundations of relativistic QFT very clearly.

Unfortunately he doesn't discuss Bell's theorem in connection with relativistic QFT in this book, and I'm not aware of any place, where he does this. If somebody has a reference by him about this, I'd be very interested in it!

2. Consider a pair of two systems A and B in an entangled state. Then there are two standard facts, that have been mentioned and can be found in the literature. The density matrix of B has all the information about the statistics of the possible outcomes of measurements on B. Any measurement on A doesn't change the density matrix of B. The question is: do you dispute any of this? If yes, can you explain why. If not, then why do you say that the statement "Measurement on A does have an effect on B. Or the cause of a result at B is the measurement on A." is interpretation independent? Actually you say it is a proven fact.

That's also not right. It depends of course on what you mean by "measurement on A". Of course, it's clear if you just prepare A and B in an entangled state and just do measurements on B, no matter what's done with A the measurement outcomes (i.e., the usual probabilistic properties of such measurements in the sense of QT) are given by the reduced density matrix, $\hat{\rho}_{B}=\mathrm{Tr}_A \hat{\rho}_{AB}$.

If, however you use experiments on A, e.g., to project out subensembles of (AB), you get a different statistical operator for B. Say you project due to $|\psi \rangle \in \mathcal{H}_A$ you get
$$\hat{\rho}_{B|A \in \psi}=\frac{\mathrm{Tr}_A (|\psi \rangle \langle|\psi| \otimes \hat{1}_{B} \hat{\rho}_{AB})}{\mathrm{Tr}_{AB} (|\psi \rangle \langle|\psi| \otimes \hat{1}_{B} \hat{\rho}_{AB})}.$$
Say $\hat{\rho}_{AB}$ is a Bell state of two photons' polarization like the singlet
$$\hat{\rho}_{AB} = |\Psi \rangle \langle \Psi|=\frac{1}{\sqrt{2}} (|HV \rangle-|VH \rangle)$$
and $|\psi \rangle=|H \rangle$, then
$$\hat{\rho}_B=\frac{1}{2} \hat{1}$$
but with $\psi=|H \rangle$ (i.e., you consider only (AB) pairs, for which you measure A to be H-polarized you get
$$\hat{\rho}_{B|A \in \Psi}=|V\rangle \langle V|.$$
That's one of the amazing features of entangled states: On the one hand if (AB) is prepared in a (pure) Bell state, the properties of B are maximally uncertain, i.e., in our example B is an ideally unpolarized photon, but still there are 100% correlations between certain properties of A and B. In our example, if you select A's with a polarization in a given direction then B's polarization concerning the same direction is the opposite, i.e., if you select A's which are H-polarized wrt. the $x$ direction, then B must be V-polarized wrt. the same $x$ direction.

 

[PeterDonis]

Yes, the total ensemble is in a pure state with the state ket of the form
$$|\Psi_{12} \rangle \otimes |\Psi_{34} \rangle,$$
where $|\Psi_{12} \rangle$ and $|\Psi_{34} \rangle$ are Bell states by preparation.

Now projecting the two photons (23) to another Bell state, you get a subensemble, where (14) are entangled.

Saying it this way is very misleading. The measurement on (23) doesn't just select a subensemble of the original ensemble. It changes the state of the 4-photon system; the 4-photon state is no longer of the form $\ket{\Psi_{12}} \otimes \ket{\Psi_{34}}$. It is now of the form $\ket{\Psi_{14}} \otimes \ket{\Psi_{23}}$.

Of course you are right in saying that this subensemble must indeed be prepared by doing this projective measurement.

By "prepared" I assume you mean the change of the overall state of the 4-photon system due to the (23) measurement, as described above. That is correct, the (23) measurement functions as a preparation of a new state of the 4-photon system. Picking out the subset of runs in which the (23) state coming out of the measurement is one particular Bell state (out of four) then selects a subensemble of the newly prepared 4-photon state. But describing it just as "selecting a subensemble" is misleading because it obfuscates that crucial fact about preparation.

 

[Simple question]

From source A, the rate might be 1 in 100 million; and the same in source B. So roughly, there might be 1 swap out of (100 million)^2 pairs. You might get 10 per seconds, to 1 in 10 minutes; obviously this varies widely based on laser strength, etc.

But we can expect the processes to be improved to reach better rate. Now that I think of it, I would venture that the upper bound would be 50% of the pairs. That is the bigger sub ensemble which also define the complement where all pair have opposite results, and thus preserve the full ensemble 1&2 non-entanglement statistics.

As 50% is also the maximum amount of expected opposite spin of any pair of unrelated photon arriving at 2&3, the universe do not have to conspire a lot to avoid FLT in this case

 

[DrChinese]

@martinbn, I answer your questions below.

I will not respond further to @Nullstein or @vanhees71 or @lodbrok in this thread until they supply specific quotes to support their positions. All 3 have provided references that wasted my time to review, and say nothing remotely similar to their positions. I consider such "references" to be the lazy man's out, and deceptive when it doesn't even support their position anyway (which none did).

My position is standard QM, as written in hundreds of papers and in papers I have referenced here and quoted verbatim. Here it is, as concisely as I can word it.

The Bell test photons which have never interacted (1 & 4) are not entangled and cannot become entangled unless* the Bell State Measurement (BSM) succeeds on the other 2 (regardless of time, place or ordering). That BSM is not considered a classical cause, but it is a "quantum" cause. That's because a classical cause *must* precede any possible effect; while causality in the quantum world does not depend on time ordering (or distance as limited by c).

The BSM is absolutely NOT simply post-selection, although the selection does herald a successful swap event. We know that because without the swap, pairs [1 & 2] and [3 & 4] are maximally entangled and monogamously so. However, with a successful swap, [1 & 4] end up maximally entangled and monogamously so. The "paradox" (which matches the predictions of QM precisely) is in the following variations:

a) Photons 1 and 4 need never co-exist in a common light cone, and yet a distant event (the BSM) causes them to become maximally entangled.
b) The BSM can be performed AFTER photons 1 and 4 are already detected and evidence a violation of a Bell inequality, which is an example of quantum nonlocality (but certainly there are other examples not involving multi-particle entanglement).
c) A BSM can even be performed BEFORE photons 1 and 4 are created, although this requires additional photons and BSMs.
d) The BSM in b) can be made to occur "after" in all references frames.

*We cannot use the word "until" in this context, because it need not precede measurement of [1 & 4].

@DrChinese Let me ask you some direct questions.

1. In which sense do you use the term non-locality? Is it meant as violations of Bell's inequality or something else. If it is only in the sense of violations of Bell's inequalities, then why do you need to talk about entanglement swapping? The violations can be demonstrated without swapping. If it is something else, can you clarify what it is? And do you claim that your references (Zeilinger, Weinberg and so on) use it also that way?2. Consider a pair of two systems A and B in an entangled state. Then there are two standard facts, that have been mentioned and can be found in the literature. The density matrix of B has all the information about the statistics of the possible outcomes of measurements on B. Any measurement on A doesn't change the density matrix of B. The question is: do you dispute any of this? If yes, can you explain why. If not, then why do you say that the statement "Measurement on A does have an effect on B. Or the cause of a result at B is the measurement on A." is interpretation independent? Actually you say it is a proven fact.

1. "Quantum nonlocality" is evidenced by a violation of a Bell inequality. Many authors simply refer to this as "nonlocality", and sometimes I do too. The reason I try to use the additional word "quantum" is because I wish to indicate that there need not be superluminal forces at work, even though there appears to be "something" that occurs superluminally. However, some interpretations have "outs" in which c is respected, so my terminology attempts to account for that. Such interpretations are, of course, what is referred to as "non-realistic" to comply with Bell.

On the other hand, any interpretation in which nonlocal correlations are explained by reference to "updating" of our knowledge while retaining locality should, IMHO, be excluded as being ruled out by swapping experiments. Not all authors yet agree with me on this point, which is part of the reason I enjoy threads like this. Always looking for someone who has a strong counter-argument, but that hasn't happened yet. So far, hand-waving and not a shred of experimental support.

Are violations of Bell inequalities synonymous with nonlocality? Violation of Bell inequalities are not the only types of quantum nonlocality, so to me the answer is "not quite". But they are experimental demonstration that nature is not local realistic, which to me is the same as saying "quantum nonlocal". Anything which is context dependent has the potential to be evidence of quantum nonlocality. Here are some other examples (outside of Bell tests) that come to mind:

a. Nonlocal wave collapse: Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurement
b. Hanbury Brown Twiss effect (bunching/anti-bunching)
c. GHZ.

Why do swapping experiments matter to the debate? In a traditional Bell test, the entangled pair share a light cone to the past, and Alice and Bob necessarily operate within the light cone of the particles they measure. They must measure their respective particles after they are entangled. This has the effect of hiding some of the eccentricities of quantum nonlocality. In swapping experiments, you have a lot more flexibility. You can demonstrate that you can entangle particles after the fact, and you can entangle particles outside each other's light cones. That's a dramatic effect!2. Hmmm, does A change as a result of a distant operation on B? First, a caveat: no experiment can precisely determine what order the hypothetical changes would occur in. A to B, or B to A? No one understands the mechanism well enough to convincingly answer that.

My answer is that A changes ("steered") as a result of a distant operation on B (acknowledging that it could be the other way around and you can't discern between the 2 possibilities). Of course, there is some interpretational spin along with this, although I will try to steer clear as best I can.

The simple answer is that by looking at A alone, nothing ever seems to change. If that is your concept of a density matrix, then you won't agree with me. But an entangled photon does not exist in isolation, it is part of a biphoton of [A+B]. That combined matrix certainly changes as a result of a successful swap, and the statistics bear this out. From an earlier reference in this thread:

"In the scenario we present here, measuring the last photon affects the physical description of the first photon in the past, before it has even been measured. Thus, the ”spooky action” is steering the system’s past. Another point of view that one can take is that the measurement of the first photon is immediately steering the future physical description of the last photon. In this case, the action is on the future of a part of the system that has not yet been created."

So apparently these authors agree with me. Virtually any swapping experiment, and many straight Bell tests, say much the same thing. Use of the the phrases "nonlocality", "quantum nonlocality" and/or "action at a distance" run through the Bell literature. The word "nonlocal" appears in the title of about 5000 scientific papers (they aren't proving locality in those papers). So I count it as 5001 for me, and 0 for you. Although 1 good reference might be enough to convince me to change my mind... but where is one that is good enough?

 

[PeterDonis]

@DrChinese, one question about the BSM that is done on photons 2&3 in the entanglement swapping experiments. If we restrict attention to photon 2&3 pairs that meet the narrow time window requirement, the "event ready" signal (i.e., the one that picks out the subset of the runs that will be assessed for entanglement of photons 1&4) is that one particular Bell state (IIRC the singlet state) is observed as the result of the BSM on 2&3. What about the other runs, where that particular Bell state is not observed as the result of the BSM on 2&3? What is observed for photons 2&3, again restricting attention to pairs that meet the narrow time window requirement? Are they in one of the other three Bell states (the experiments as they are currently set up just don't measure which one)?

We may have gone through this in a previous thread but I can't recall for sure.

 

[DrChinese]

@DrChinese, one question about the BSM that is done on photons 2&3 in the entanglement swapping experiments. If we restrict attention to photon 2&3 pairs that meet the narrow time window requirement, the "event ready" signal (i.e., the one that picks out the subset of the runs that will be assessed for entanglement of photons 1&4) is that one particular Bell state (IIRC the singlet state) is observed as the result of the BSM on 2&3. What about the other runs, where that particular Bell state is not observed as the result of the BSM on 2&3? What is observed for photons 2&3, again restricting attention to pairs that meet the narrow time window requirement? Are they in one of the other three Bell states (the experiments as they are currently set up just don't measure which one)?

We may have gone through this in a previous thread but I can't recall for sure.

Good questions. The answers are a bit complicated, and I occasionally get confused between the various permutations, so don't shoot me if a get a + or a - backwards...

1. A good reference (with a few quotes below) is https://arxiv.org/pdf/0809.3991.pdf , see especially the top middle of figure 1. I will use the [2 & 3] pair labeling for the Bell State Measurement (BSM), and the [1 & 4] pair for the Bell test (as in the reference). Everything assumes photons that are linear polarized, all initial pairs [1 & 2] and [3 & 4] entangled. We ignore the many cases where there are clicks at [1] or [4] but do not match a successful BSM on [2 & 3]. BSM successes are rare, since the [1 & 2] pairs come at random intervals, as do the [3 & 4] pairs. For a successful BSM, both need to fire simultaneously*. That might happen perhaps once every 10 seconds.

2. As you know, there are 4 Bell States which may occur during a BSM. They occur with roughly equal likelihood. Also, the initial pairs [1 & 2] and [3 & 4] can themselves be created as perfectly correlated (Type I PDC) or perfectly anti-correlated (Type II PDC). The experimenters themselves know which is which, but by using the same Type on both pairs, there is no adjustment necessary.

• Psi+ for [2 & 3]: Photons [1 & 4] will be perfectly correlated.
• Psi- for [2 & 3]: Photons[1 & 4] will be perfectly anti-correlated.
• Phi+ for [2 & 3]: cannot be distinguished from Phi-.
• Phi- for [2 & 3]: cannot be distinguished from Phi+.

An important factor is that not all of the 4 states can be simultaneously distinguished via BSM. "This is the optimum efficiency possible with linear optics."-Zeilinger et al [J. Calsamiglia and N. Lutkenhaus, Appl. Phys. B (2001)]. As a general rule, the Psi+ and Psi- states can be be distinguished using a beam splitter (BS), 2 polarizing beam splitters (let's label PBS1 and PBS2), and 4 detectors (let's label as PBS1h, PBS1v, PBS2h, PBS2v. Each of the 2 BS outputs are routed to a PBS, and each of the 2 PBS outputs are routed to a detector. Keep in mind, this is all part of the BSM apparatus, used to initiate/herald/cause the swap action.

3. So to answer your question: the statistical split of possible outcomes is approximately as follows:

• 25%: The simultaneous* clicks of PBS1h and PBS1v, or PBS2h and PBS2v, heralds a successful Psi+ swap.
• 25%: The simultaneous* clicks of PBS1h and PBS2v, or PBS1v and PBS2h, heralds a successful Psi- swap.
• 50%: Simultaneous* clicks in any of 4 other combos (such as PBS1h and PBS2h, etc) indicate a Phi+ or Phi-, but you won't know which. There is no way to make sense of the [1 & 4] outcomes as part of the Bell test porting. That makes these useless for consideration. These are not counted, even though they indicate a successful swap.

The approach does vary from one swapping experiment to another. Some experiments look at the Psi- Bell state only, while others look for both Psi states. All approaches ignore at least 2 of the 4 states. It is worthy to remind everyone: in all cases the [2] and [3] photons have the opportunity to overlap and/or interact and/or interfere. They must be indistinguishable in time, so you won't know the source for any of the BSM clicks.

4. What is important to understand is: all qualifying events are included for the CHSH calculation (or whatever statistics are being calculated) as long as the appropriate clicks occur at the BSM apparatus**. They assume that indicates a successful swap occurred, even if it didn't. So the entanglement measure (S) won't be overstated by any swap failures.

"The specific state of photons 1 and 4 after entanglement swapping depends on the result of the BSM, which can either be ψ + or ψ −. The relevant CHSH inequalities for these cases are S=..."

The result of this 2009 experiment: "We achieve a clear violation of the CHSH inequality with Sψ− = 2.37 ± 0.09 and Sψ+ = 2.38 ± 0.09. In all cases the CHSH inequality [S<=2] is violated by more than four standard deviations."

Cheers,

-DrC*Simultaneous meaning: within your narrow time window requirement. That might be on the order of 10 picoseconds.
** Assuming there are matching clicks for the [1 & 4] photons so their match coincidence can be counted as part of the Bell test.

 

[PeterDonis]

Some experiments look at the Psi- Bell state only, while others look for both Psi states. All approaches ignore at least 2 of the 4 states.

Ok, that's what I thought. Thanks for the detailed clarification!

 

[martinbn]

@martinbn, I answer your questions below.

Thank you!

If I understood your answer correctly, there is not difference of opinions about point 1. It is just a matter of phrasing that causes the argument/discussion. I still don't see the need for swapping. In fact it suggest the opposite. If the measurement of (23) is done after 1 and 4 no longer exists. Then it is very strange (even if it is a matter of interpretation) to say that the act of measurement of (23) does something physical to (14)!!

About point 2. I cannot agree (which is the same as the second part of 1.). May be it is still just a language problem rather than content but you say this

My answer is that A changes ("steered") as a result of a distant operation on B

It there is no way for the person at A to tell bay experiment, then for me this is interpretation dependent. And therefore I cannot see why you insist on it as if it is not interpretation dependent!

So apparently these authors agree with me. Virtually any swapping experiment, and many straight Bell tests, say much the same thing. Use of the the phrases "nonlocality", "quantum nonlocality" and/or "action at a distance" run through the Bell literature. The word "nonlocal" appears in the title of about 5000 scientific papers (they aren't proving locality in those papers). So I count it as 5001 for me, and 0 for you. Although 1 good reference might be enough to convince me to change my mind... but where is one that is good enough?

This is irrelevant. No one argues whether these terms are used. But whether any/all experiments show that there is any nonlocality in a sense different of "violation of Bell inequality".

 

[vanhees71]

@martinbn, I answer your questions below.

I will not respond further to @Nullstein or @vanhees71 or @lodbrok in this thread until they supply specific quotes to support their positions. All 3 have provided references that wasted my time to review, and say nothing remotely similar to their positions. I consider such "references" to be the lazy man's out, and deceptive when it doesn't even support their position anyway (which none did).

If you don't want to read short papers (PRL!) about what you want to discuss, it's of course useless to start discussing at all. I don't write a textbook about basic QED/quantum optics in form of forum postings.

My position is standard QM, as written in hundreds of papers and in papers I have referenced here and quoted verbatim. Here it is, as concisely as I can word it.

QM is not appropriate to discuss about locality, because that's a notion referring to relativistic theories, i.e., you have to discuss questions of locality within relativistic theories, and the only working relativistic QT is local (sic!) relativistic QFT.

 

[vanhees71]

@DrChinese, one question about the BSM that is done on photons 2&3 in the entanglement swapping experiments. If we restrict attention to photon 2&3 pairs that meet the narrow time window requirement, the "event ready" signal (i.e., the one that picks out the subset of the runs that will be assessed for entanglement of photons 1&4) is that one particular Bell state (IIRC the singlet state) is observed as the result of the BSM on 2&3. What about the other runs, where that particular Bell state is not observed as the result of the BSM on 2&3? What is observed for photons 2&3, again restricting attention to pairs that meet the narrow time window requirement? Are they in one of the other three Bell states (the experiments as they are currently set up just don't measure which one)?

We may have gone through this in a previous thread but I can't recall for sure.

As described in the PRL, I've quoted several times now, they do a projection to the polarization-singlet state of the photon pair (23), i.e., they select the events, where they select those events, where they register these 2 photons 2&3 at two different detectors in coincidence. This implies that these two photons are found to be in the polarization-singlet state. Given the initial state of the 4 photons, in the so selected subensemble the photons 1&4 are in a Bell state, although they never where in direct causal contact.

To see this, write the original state ket in the form of Eq. (4) of the paper:
$$|\Psi \rangle=\frac{1}{2} (|\Psi^+ \rangle_{14} |\Psi^{+} \rangle_{23} + \Psi^- \rangle_{14} |\Psi^{-} \rangle_{23} +|\Phi^+ \rangle_{14} |\Phi^{+} \rangle_{23} +|Phi^- \rangle_{14} |\Phi^{-} \rangle_{23}).$$
If (23) is registered at different detectors, you know they are in the state $|\Psi^- \rangle_{23}$, i.e., in the polarization-singlet state, and this projection thus gives
$$|\Psi' \rangle=|\Psi^- \rangle_{23} \langle \Psi^-|_{23} \otimes \hat{1}_{14} = \frac{1}{2} |\Psi^- \rangle_{23} |\Psi^- \rangle_{14},$$
and this happens with the probability
$$\langle \Psi'|\Psi' \rangle=\frac{1}{4}.$$
For this subensemble then the reduced state for the pair (14) is the pure maximally entangled Bell state $\hat{\rho}_{14}=|\Psi^-\rangle_{14} \langle \Psi^-|_{14}$.

For the cases, where photon 2&3 are not registered at different detectors, you have no projection into a definite Bell state, and thus for the complementary subensemble photons 1&4 are not entangled, because you have
$$|\Psi'' \rangle=(\hat{1}_{23} \otimes \hat{1}_{14}-|\Psi^- \rangle_{23} \langle \Psi^-|_{23} \otimes \hat{1}_{14})=\frac{1}{2} (|\Psi^+ \rangle_{23} |\Psi^{+} \rangle_{14} +|\Phi^+ \rangle_{23} |\Phi^{+} \rangle_{14} +|Phi^- \rangle_{23} |\Phi^{-} \rangle_{14}).$$
The reduced state of pair (14) is given by partially tracing out over the pair (23):
$$\mathrm{Tr}_{23} |\Psi'' \rangle \langle \Psi'' \rangle=\frac{1}{3} (|\Psi^{+} \rangle_{14} \langle \Psi^+|_{14}+ |\Phi^{+} \rangle_{14} \langle \Phi^+|_{14} + |\Phi^{-} \rangle_{14} \langle \Phi^-|_{14}).$$

 

[martinbn]

For the cases, where photosn 2&3 are not registered at different detectors, you have no projection into a definite Bell state, and thus for the complementary subensemble photons 1&4 are not entangled or at least not maximally entangled. If needed, I can calculate the concrete state this subensemble is prepared in.

What one can do in the other cases (assuming that 1 and 4 are still around) is to send (through a classical channel) the result of the measurement of (23) to those at 1 and 4. Then they can pass them through the appropriate gate. This way the whole (14) ensemble will be entangled. It is a quantum teleportation scenario.

 

[Simple question]

I still don't see the need for swapping.

Swap is a time dependent notion, there is a before and an after:
1+2 and 3+4 become 1+4 and 3+2, that is : 4 and 2 have swapped place.
How could an entanglement swapping experiment be done without swapping ?

It there is no way for the person at A to tell bay experiment, then for me this is interpretation dependent. And therefore I cannot see why you insist on it as if it is not interpretation dependent!

There are plenty of test both A and B can make, once they compare result. With simple Bell experiment or more complex one involving "swapping". No interpretation needed.

Another fact: they both agree they did obtain locally some information about a space-like separated events. When it is no surprising when unboxing classical socks, it is spooky when unboxing random quantum spin, as Bell demonstrated.

 

[martinbn]

Swap is a time dependent notion, there is a before and an after:
1+2 and 3+4 become 1+4 and 3+2, that is : 4 and 2 have swapped place.
How could an entanglement swapping experiment be done without swapping ?

You are not following the conversation. I asked why mention swapping if you want to show violation of Bell inequality. You don't need swapping for that.

There are plenty of test both A and B can make, once they compare result. With simple Bell experiment or more complex one involving "swapping". No interpretation needed.

How is that related to what I am saying! Again, if you are not following, then reread the posts.

Another fact: they both agree they did obtain locally some information about a space-like separated events. When it is no surprising when unboxing classical socks, it is spooky when unboxing random quantum spin, as Bell demonstrated.

Same here.

 

[DrChinese]

You are not following the conversation. I asked why mention swapping if you want to show violation of Bell inequality. You don't need swapping for that.

Ask and you shall receive!

As I and others have said: Using swapping to create entangled pairs for Bell tests is absolutely an important advance on many levels.

1. The entangled pair is heralded, something that basic PDC won't do.
2. The technique can be used to create quantum networks across arbitrarily large distances.
3. Some technical loopholes can be closed by using fully independent sources that are distant.

And for me, these above all others:
4. Some of the attempts to create local models can be ruled out by these experiments. An entangled Bell pair from distant sources cannot be explained by any purely local (Einsteinian local) model.
5. The limits of classical causality can be explored/defined by quantum operations that defy the usual notions of ordering. Specifically: operations in the future that *appear* to change the past, as well as operations in the past that change the future in a distant location.

I now judge all interpretations through the lens of the entanglement swap variations I have written about here and in other threads. Many interpretations no longer stack up. Compared to the experimentalists in this area, I am a bit late to this realization. But I can see that many others have not yet warmed up to this. However, once you wrap your head around the newest experiments (from the past 5-10 years or so), it should be clear that QM* involves mechanisms that defy almost any hint of a classical description.

For example: This thread is about the de Raedt simulations. Obviously, these models must be thrown out due to the kind of Bell pairs which derive from distant swapping.

*Keeping in mind that the umbrella of QFT adds little to our understanding of the quantum mechanical world. That is not a criticism of QFT, which of course is the gold standard. But apparently nature defies all attempts at causal ordering on every level.

 

[gentzen]

I now judge all interpretations through the lens of the entanglement swap variations I have written about here and in other threads. Many interpretations no longer stack up. Compared to the experimentalists in this area, I am a bit late to this realization. But I can see that many others have not yet warmed up to this.

This way of thinking sounds "dangerous" to me: The results of those experiments with entanglement swap variations are in perfect agreement with the predictions of QM. All interpretations of QM have to give the same predictions as QM (for all practical purposes). Otherwise, they are different theories and not merely interpretations. So if you believe that you can exclude certain interpretation based on the results of those experiments, then there seems to be a high risk that you are misunderstanding that specific interpretation, or that you are "overinterpreting" the results of those experiments.

However, once you wrap your head around the newest experiments (from the past 5-10 years or so), it should be clear that QM* involves mechanisms that defy almost any hint of a classical description.

Of course, a classical description is inappropriate. What these newest experiments may add is to partially undo the damage done by all those Schrödinger's cat, Wigner's friend, or Frauchinger-Renner thought experiments, which are not real experiments (and will never be), and consequently are not predictions of QM either. So now we know that Quantum teleportation and Superdense coding are more than just unreal thought experiments.

I bring-up Superdense coding here, because the fact that a single qubit "in context" can transmit two classical bits hints at one specific place where our classical intuition risks to get lost. That a single qubit can encode a single classical bit even "without context", is relatively easy to grasp. But that a single qubit "in context" can encode two classical bits, and also that two classical bits can encode a single qubit "in context" (as demonstrated by Quantum teleportation), that is what is hard to swallow for our classical intuition: Isn't the single qubit described by three independent real parameters? How should two classical bits ever be enough to encode it? One possible answer may be that each single experiment can only provide a single "context", and that therefore the "context" is fixed with respect to the experiment. And because the "context" cannot vary, the three independent real parameters lose their significance. And then one can show that only two classical bits remain. Maybe there are better answers, but I guess any answer trying to explain this will remain hard to swallow.

 

[martinbn]

Ask and you shall receive!

As I and others have said: Using swapping to create entangled pairs for Bell tests is absolutely an important advance on many levels.

1. The entangled pair is heralded, something that basic PDC won't do.
2. The technique can be used to create quantum networks across arbitrarily large distances.
3. Some technical loopholes can be closed by using fully independent sources that are distant.

I would say that everyone would agree with this.

And for me, these above all others:
4. Some of the attempts to create local models can be ruled out by these experiments. An entangled Bell pair from distant sources cannot be explained by any purely local (Einsteinian local) model.
5. The limits of classical causality can be explored/defined by quantum operations that defy the usual notions of ordering. Specifically: operations in the future that *appear* to change the past, as well as operations in the past that change the future in a distant location.

My impression is that this was generally accepted even before teleportation/swapping experiments.

I now judge all interpretations through the lens of the entanglement swap variations I have written about here and in other threads. Many interpretations no longer stack up. Compared to the experimentalists in this area, I am a bit late to this realization. But I can see that many others have not yet warmed up to this. However, once you wrap your head around the newest experiments (from the past 5-10 years or so), it should be clear that QM* involves mechanisms that defy almost any hint of a classical description.

For me, personally, that QM doesn't allow any hint of classical description is evident already in QM itself from the 1920s, 1930's. The experiments only confirm that.

I have to say that for me, entanglement swapping shows that there is no action at a distance. In other words the nonlocality of QM is not some sort of classical action at distance type of nonlocality. After all if the two particles didn't exit simultaneously (in any convention) then how could they act on/affect each other instantaneously!

 

[Simple question]

The results of those experiments with entanglement swap variations are in perfect agreement with the predictions of QM.

But is it really ? QM does define entanglement, which was obviously theoretically applicable on paper to state of particle "prepared" in space-like region. Writing it on paper is easy but realizing it physically is more difficult. But now it is done.

My opinion is that the danger is is to say the QM can make any prediction, on how the 2&3 process will happen. It only predict 50% on average... which is true, but not more useful than a coin toss. But NATURE does way better than that, and it is not classical nor causal.

If I understood it correctly, QFT and micro-causality explicitly forbid anything space-like to have any predictive(or even retro) effect on the solution of QM local "prediction". Fine.
But does it not mean the Bell's theorem is (and was) intended to show that if NATURE (the territory) (not QM (the map)), is indeed compatible with QM "logic", then NATURE contains NON-LOCAL "processes" ?

So I think it follows that QM is incomplete, at least for those that think that QM must be a local-causal only theory (in SR sense), and that anything else is irrelevant, and can be safely ignored, or worse deemed a "interpretation issue".

It's not. Those non-local physical processes are (or will be) used to protected channel of communication.

 

[vanhees71]

If I understood it correctly, QFT and micro-causality explicitly forbid anything space-like to have any predictive(or even retro) effect on the solution of QM local "prediction". Fine.
But does it not mean the Bell's theorem is (and was) intended to show that if NATURE (the territory) (not QM (the map)), is indeed compatible with QM "logic", then NATURE contains NON-LOCAL "processes" ?

Bell's theorem, i.e., the validity of Bell's inequalities is derived from two assumptions: "locality" and "realism". Locality simply means that the setting of the hidden variables in the very beginning determines their setting once and for all, including their probabilistic description in terms of standard probability theory. It's a very weak condition, and the more constraining condition of "locality" in the sense of "microcausality" of relativistic QFT of course, fulfills this condition.

Realism means that all observables always take determined values given the values of the hidden variables, i.e., the probabilistic description is necessary only because of our ignorance of these values due to the ignorance about the hidden variables, and thus the statistics is in terms of standard probability theory for all observables given any probability distribution of the hidden variables (see Weinberg, Lectures on Quantum Mechanics, 2nd edition).

The latter is of course not fulfilled for any type of QT, including relativistic local QFT. Since relativistic local QFT fulfills for sure the locality assumption and violates Bell's inequalities in accordance with the observations made in Bell tests, it must be "realism" which is violated by QT and obviously also by Nature.

So I think it follows that QM is incomplete, at least for those that think that QM must be a local-causal only theory (in SR sense), and that anything else is irrelevant, and can be safely ignored, or worse deemed a "interpretation issue".

Relativistic local QFT is perfectly local and causal. Causality only means that if the state of the system is given in the past it's uniquely determined in the future (given the dynamical laws of the theory under consideration), and that's the case for all QTs, even in the more restricted sense that there's not even memory, i.e., it's sufficient to know the state at a given point in time to know the state at any later time.

Whether or not QT is "complete" is a pretty empty question. At least in one sense it's incomplete, because there's no satisfactory quantum description of the gravitational interaction ("quantum gravity"). As any so far known physical theory it thus has its restricted realm of applicability.

 

[gentzen]

But does it not mean the Bell's theorem is (and was) intended to show that if NATURE (the territory) (not QM (the map)), is indeed compatible with QM "logic", then NATURE contains NON-LOCAL "processes" ?

Bell's theorem and Bell's inequality are typical normal incremental science, clarifying questions raised by EPR and Bohmian mechanics. And the refinements of Bell's inequality and experiments based on it too are typical incremental science.
They are mostly intended to answer specific precise questions raised by previous research, and only tangentially intended to show that "NATURE (the territory)" would be this or that.

The intention was to make clear unambiguous progress (even if small and incremental), not to open yet another "interpretational can of worms".

 

[vanhees71]

Indeed, it translated the vague metaphysical speculation of EPR into a clear scientific prediction about "local realistic theories" to be tested against (!!!) QT. In this way it promoted vague philosophical quibbles of EPR and made interpretational issues a scientifically decidable problem.

 

[Simple question]

The latter is of course not fulfilled for any type of QT, including relativistic local QFT. Since relativistic local QFT fulfills for sure the locality assumption and violates Bell's inequalities in accordance with the observations made in Bell tests, it must be "realism" which is violated by QT and obviously also by Nature.

So you are saying that QFT is incomplete because it is unrealistic to use standard probabilistic theory ? I agree that this is a perfectly coherent take on QFT

Whether or not QT is "complete" is a pretty empty question.

Well it depends on your philosophy. If you think science is not about explaining/computing/predicting what happens in nature, than yes I suppose you can think "it is an empty question".
Others think we should find how non-local correlation happens, and not just say: because this is "unrealistic" (as per Bell's)

At least in one sense it's incomplete, because there's no satisfactory quantum description of the gravitational interaction ("quantum gravity").

I always thought that QFT (and all other QM flavors) was only about explaining Quantum effect (especially at high energy where space-time curvature may prove important), and cannot care less about (nor-be appropriate for) apple falling or even bigger object

 

[Simple question]

They are mostly intended to answer specific precise questions raised by previous research, and only tangentially intended to show that "NATURE (the territory)" would be do this or that.

I agree with you, I am only tangentially interested in what nature is and more interested in what we deduce about our "maps", their domain of applicability, their completeness is one such characteristic.

I would like that map to "contains" what nature does, like non-local correlation, because we know, because of experiment, that nature is un-realistic in Bell's sense, and QFT deny the possibility to explain(and compute) non-local correlation.

Well, we can use those non-local physical correlation anyway. With enough certainty (maybe not 100%, but above 50%) to base security system around it. If QFT proponent are content with 50% confidence, then well, this is fine by me. What's not is for them to call this "complete", or to deem them "interpretation" issue.

The intention was to make clear unambiguous progress (even if small and incremental), not to open yet another "interpretational can of worms".

I really do agree 100% with you. This is not about "interpretation", but doing hard science, and closing some loophole "found" in Bell's inequality experimental verification.

 

[vanhees71]

So you are saying that QFT is incomplete because it is unrealistic to use standard probabilistic theory ? I agree that this is a perfectly coherent take on QFT

No, Nature follows the predictions of Q(F)T not the predictions of local realistic hidden-variable theories. In this sense Q(F)T is a complete description of the observed phenomena within its realm of applicability.

Well it depends on your philosophy. If you think science is not about explaining/computing/predicting what happens in nature, than yes I suppose you can think "it is an empty question".
Others think we should find how non-local correlation happens, and not just say: because this is "unrealistic" (as per Bell's)

Science is about objectively observable quantifiable phenomena and finding mathematical theories to describe these phenomena. It's not answering questions outside this methodology.

I always thought that QFT (and all other QM flavors) was only about explaining Quantum effect (especially at high energy where space-time curvature may prove important), and cannot care less about (nor-be appropriate for) apple falling or even bigger object

Q(F)T is describing everything known today except gravity, from the subatomic-few-particle level as investigated in collisions at particle accelerators ("vacuum QFT") to composite systems (atomic nuclei, atoms, molecules, condensed matter) ("many-body Q(F)T").

 

[Simple question]

No, Nature follows the predictions of Q(F)

No, QFT probalilistcally predic what nature may do (it is the other way arround), and by your own admission:
** can NOT be use to predict space-like correlation, witch is what swapping is all about.

and not the predictions of local realistic hidden-variable theories.

I've never heard of any such theory, and I am pretty sure Bell's proved it is not possible to come up with one. Why are you bringing that up ?

In this sense Q(F)T is a complete description of the observed phenomena within its realm of applicability.

.. which does not contain space-like events if I understand you correctly. Hence it is incomplete, because those non-local phenomena are observed, in the lab.

 

[vanhees71]

Bell's theorem is about local realistic hidden-variable theories, and the strength in fact is that you don't need to specify a definite one.

I don't know, what you mean QFT doesn't contain predictions about space-like separated events. It predicts, e.g., by construction (microcausality constraint) that space-like separated events cannot be causally connected.

 

[DrChinese]

This way of thinking sounds "dangerous" to me: The results of those experiments with entanglement swap variations are in perfect agreement with the predictions of QM. All interpretations of QM have to give the same predictions as QM (for all practical purposes). Otherwise, they are different theories and not merely interpretations. So if you believe that you can exclude certain interpretation based on the results of those experiments, then there seems to be a high risk that you are misunderstanding that specific interpretation, or that you are "overinterpreting" the results of those experiments.

Yikes, I don't wanna do anything dangerous...

The experimental results match QM, so all is fair in demanding interpretations meet these higher bars as well. I absolutely do not agree all interpretations have mechanisms that can be considered equivalent to QM. If an interpretation claims a biphoton (system of 2 entangled photons) must evolve separately because it cannot be created as a single system with spatial extent: that's unacceptable. If an interpretation denies monogamy of entanglement: that's unacceptable. If an interpretation claims a future distant measurement context cannot influence the results of a Bell test, that too is unacceptable. In other words: from Bell we learned nature is not both local and realistic (causal), but now we know there are additional hoops to jump through. I want to see how each interpretation handles these hoops, and if they deny the need to do so... well, scratch that.

@vanhees71 says in post #71: "Relativistic local QFT is perfectly local and causal." That's wrong on so many levels (ignoring that Bell nixed that long ago). AFAIK he is the only person on the planet that would write that statement. But I have promised PeterDonis that I will stop debating the point, as vanhees71 uses "local" differently than I do. 'Nuff said. I consider QFT a superset of QM, but regardless it is impossible that there is Einsteinian causality as part of any viable theory... even QFT.

And with interpretations such as MWI, trying to picture the how the "splitting" occurs when measurements are occurring all over the place (in a swapping network) makes my head spin. So I don't believe all interpretations reproduce the predictions of QM; they just claim to. I acknowledge that all authors in the field don't see it the same as I, but some have realized that there are interpretations that need re-examination. I freely admit that I am not the best student of MWI and Bohmian Mechanics. But none of the "updating our knowledge" interpretations make any sense in the new experimental order.

Clearly, an action on A here changes distant B's state - there is no updating of our knowledge of a pre-existing state. And just as clearly, the change in B's state can be made to occur before or after the action on A. I don't see that any experimentalist working with swapping would see it otherwise.

 

[PeterDonis]

I don't believe all interpretations reproduce the predictions of QM; they just claim to.

All interpretation use the same (or equivalent) math to make predictions. That's why they all make the same predictions.

Different interpretations tell very different stories about why the predictions are what they are. Nobody thinks the stories told by all interpretations are equally plausible. But not everyone has the same rank ordering, so to speak, of how plausible the various stories are. And at the end of the day, they're all just stories, which cannot be tested by experiment since they all agree on what the experimental results are. That's why QM interpretation is still an open field after a century of QM.

The other difference between QM interpretations is what kind of more comprehensive theories they suggest. For example, collapse interpretations suggest some kind of "objective collapse" theory like the GRW stochastic collapse theory. This is a different theory, not just a different interpretation of QM, because it makes different predictions from standard QM in certain situations. Unfortunately, this theory, AFAIK, has been ruled out because its predictions have not panned out. But if there is ever going to be any kind of resolution to the QM interpretation debate, it will have to be along such lines as these, where some interpretation leads to a more comprehensive theory that does pan out.

 

[Simple question]

but some have realized that there are interpretations that need re-examination.

I wonder what @Demystifier would say about how Bohmian "realistic" trajectories could or would span those swapping network.

Clearly, an action on A here changes distant B's state

To avoid confusion I would say: an action at A make it correlated to a distant B's state. That in itself is spooky enough

 

[gentzen]

If an interpretation claims a future distant measurement context cannot influence the results of a Bell test, that too is unacceptable. In other words: from Bell we learned nature is not both local and realistic (causal), but now we know there are additional hoops to jump through.

I guess you are "overinterpreting" here, in the sense that you believe that the meaning of those word would be less ambiguous than they actually are. Your first sentence reads as if you believed that one could prove a causal influence from a "future distant measurement context" to "the results of a Bell test" performed in its timelike past. Or maybe just spacelike separated. But in any case, correlations in QM often come without a "provable" causal direction, and those swapping experiments don't exhibit such a direction either.

The "(causal)" behind "realistic" doesn't reduce ambiguity either. I would even say that it makes it even worse, because the meaning of "realistic" in the context of Bell's theorem is at least somewhat established, while the meaning of "causal" is much less discussed in that context.

And I am not convinced that the entanglement swap experiments provide "additional hoops to jump through" which are not already required by Quantum teleportation and Bell inequality violations alone.

But none of the "updating our knowledge" interpretations make any sense in the new experimental order.

Clearly, an action on A here changes distant B's state - there is no updating of our knowledge of a pre-existing state. And just as clearly, the change in B's state can be made to occur before or after the action on A. I don't see that any experimentalist working with swapping would see it otherwise.

And here my guess is that you are misunderstanding those "knowledge" interpretations. I am thinking here of interpretations defended by Rudolph Peierls, by QBists, or by some advocates of Copenhagen (like Heisenberg). Which doesn't mean that those interpretations are unproblematic, but they are neither easy to understand nor easy to destroy.

 

[DrChinese]

1. I wonder what @Demystifier would say about how Bohmian "realistic" trajectories could or would span those swapping network.2. To avoid confusion I would say: an action at A make it correlated to a distant B's state. That in itself is spooky enough

1. There are groups who understand the issues with Bohmian trajectories much better than I. I try to stay away from attacks on Bohmian type theories simply because they are explicitly nonlocal, so there should be some angle for them to stay in the game.

2. I specifically meant it how I phrased it. The swap "causes" (where time ordering not relevant) the [1 & 2] monogamous entanglement to become [1 & 4] monogamous entanglement. [1 & 4] become a new quantum system (a biphoton). The state of [1] and [4] changed. Period. And what caused it was an quantum action at a distant place. That is spooky action at a distance, regardless of what anyone's feelings are about those words.

3. And I am not convinced that the entanglement swap experiments provide "additional hoops to jump through" which are not already required by Quantum teleportation and Bell inequality violations alone.

3. Swap = teleportation, so no disagreement. I think Bell + teleportation is definitely a higher bar than Bell alone. Again, this thread is about the De Raedt "local realistic" simulation - and you certainly don't need to waste time looking at a simultation that purports to mimic PDC entanglement when you have entanglement between particles that have never interacted. For their model, it's case closed.

4. But in any case, correlations in QM often come without a "provable" causal direction, and those swapping experiments don't exhibit such a direction either.

4. I couldn't agree more. And that's precisely my point as to why interpretations preserving Einsteinian causality are doomed. Causal direction is completely ambiguous in actual experiments. The only way to preserve causality is by assumption. Which is to say there is no support for it in quantum events.

5. And here my guess is that you are misunderstanding those "knowledge" interpretations. I am thinking here of interpretations defended by Rudolph Peierls, by QBists, or by some advocates of Copenhagen (like Heisenberg). Which doesn't mean that those interpretations are unproblematic, but they are neither easy to understand nor easy to destroy.

5. "According to QBism, many, but not all, aspects of the quantum formalism are subjective in nature. For example, in this interpretation, a quantum state is not an element of reality—instead it represents the degrees of belief an agent has about the possible outcomes of measurements. Regarding quantum states as degrees of belief implies that the event of a quantum state changing when a measurement occurs—the "collapse of the wave function"—is simply the agent updating her beliefs in response to a new experience. Second, it suggests that quantum mechanics can be thought of as a local theory, because the Einstein–Podolsky–Rosen (EPR) criterion of reality can be rejected. The EPR criterion states, "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

The above, from Wikipedia, shows exactly how QBism is NOT equivalent to QM - despite its claims otherwise. There is no sense that QBism can describe perfect correlations of distant particles that have never been in contact as any form of "locality" or as being subjective in any way. There is no "updating" of knowledge, and I am surprised that anyone would assert there is with a straight face. It is a fact, one all observers agree on: perfect correlations (probability=100%) of distant particles without any possibility of Einsteinian interaction. There are no degrees of belief! There is no "agent"! Sure, it may be non-realistic, but if so, there still needs to be an explanation of how the perfect correlations of distant particles arise.

Keep in mind that the entire purpose of an interpretation like this is to somehow preserve Einsteinian locality (i.e. there is no action at a distance). But when we can teleport an unknown state from point A to point B without regard for c, then that objective becomes kaput.

-DrC

 

[lodbrok]

The BSM is absolutely NOT simply post-selection, although the selection does herald a successful swap event. We know that because without the swap, pairs [1 & 2] and [3 & 4] are maximally entangled and monogamously so. However, with a successful swap, [1 & 4] end up maximally entangled and monogamously so.

Heralding in the context of these experiments means to signal that an event meets a particular criterion. It is a filtration or selection flag. The following analogy is appropriate:

For each iteration (#i), you send randomly coloured pairs of socks [1&2] and [3&4] to two different remote locations. Midway through the trip, the pairs are separated so one member of each pair (1 and 4) goes to station A, and the other (2, 3) goes to station B. At station B, a BSM experiment is performed, which in this analogy is equivalent to asking the question "are both socks the same colour?". If the answer is "Yes", the supervisor writes down the number (#i) in his journal (aka "Supervisor's Herald"). If the answer is "No", he ignores it and continues evaluating pairs of socks [2&3] as they come in for many thousands of iterations.

Back at station A, another supervisor has been evaluating incoming pairs [1&4] of socks independently also and keeping the results in a table where she writes down the numbers (#i) next to her results "Yes" or "No". Based on the distances from the socks factory to stations A and B, these "measurements" may happen at different times with A happening before B or vice versa.

The day after the experiments, the supervisors both travel to a third location, taking just their journals with them. Supervisor B notes that the entries in her table are completely random switches between "Yes" and "No". Supervisor A says, "let us filter your spreadsheet and use just the rows with just the numbers from my Herald!". After doing that, they find that all those rows are always "Yes".

Does this mean anything was transferred from any particular pair of socks to any other pair of socks? No! It simply means you are using the information from the [2&3] interaction to post-select a subset from the [1&4] interaction data that would show a correlation, despite the fact that the full [1&4] data does not show any such correlation. In other words, the BSM measurement on [2&3] "heralds" a successful bell state between [2&3] and by extension their entangled siblings [1&4].
The correlation between the [1&4] subset can only be obtained when the information from the "Supervisor's Herald" is used to select the subset of the results from station A. Therefore any influence travels only as fast as it takes for supervisors, A and B to meet and compare notes.

 

[Demystifier]

I wonder what @Demystifier would say about how Bohmian "realistic" trajectories could or would span those swapping network.

Sorry, I didn't follow the discussion so I don't know what is swapping network. Can you briefly explain it to me, or point to the post where this is clearly explained?

But more generally, the details of microscopic Bohmian trajectories are pretty much irrelevant. What matters are the macroscopic trajectories of pointers of the measuring apparatuses, for details see the paper linked in my signature.

 

[Fra]

But none of the "updating our knowledge" interpretations make any sense in the new experimental order.

Not sure if this is relevant to the thread, but it seems relevant for me in order to understand your reasoning, so it makes me curious what your own interpretation or opinion is?

There is no sense that QBism can describe perfect correlations of distant particles that have never been in contact as any form of "locality" or as being subjective in any way. There is no "updating" of knowledge, and I am surprised that anyone would assert there is with a straight face.

One problem of standard qbism that even I acknowledge, is that it does not treat the interaction of the agents. This failure is essentially similar to the problem of a fixed classical background (ie which does not interact with backgrounds of other observers).

But I think any ambitious interpretation has a vision of howto progress from the basic stance, that defines the interpretation. But those visions are then no longer just interpretations. That basic qbist stance itself, I agree, solves nothing!

/Fredrik

 

[gentzen]

Again, this thread is about the De Raedt "local realistic" simulation - ... For their model, it's case closed.

Yeah, at least there are excellent reasons to doubt that such a thing could work. Together with existing papers that try to explicitly disprove it, I am fully confident to dismiss it, case closed.

And of course, I am aware that I tried here (in this thread) to provide an „answer“ to the question you raised in the (now closed) thread:
https://www.physicsforums.com/threa...-of-a-quantum-operation-called-a-bsm.1047772/

I found that an interesting question back then, I didn‘t knew the answer, and I postponed following that thread until I had enough time to deeply dive into it. But when that time came, the thread was already closed. And so I didn‘t dive into it.

What has changed now is that I had the impression that your „monogamy of entanglement“ argument did convince PeterDonis. But I still couldn‘t see how it would change the things why I was unsure about the correct answer. Additionally, your „unconditional“ rejection of „locality“ raised for me the question, of how one could even argue in general (for or against anything), if decomposition into „local“ pieces is rejected. This gave me the idea to decompose the entanglement swapping experiment into two Quantum teleportations, and one Bell experiment:

3. Swap = teleportation, so no disagreement. I think Bell + teleportation is definitely a higher bar than Bell alone.

In fact, the teleportations used for Swap are „poor man‘s“ teleportations, because they only use 1 out of the 4 possible measurement results (for each teleportation), and because there are two teleportations, only 1 out of 16 events is usable. (That‘s why I called it „poor man…“.) But there was another question for me, namely am I even allowed to assume that „poor man‘s“ teleportation still works, especially if I admit that you might be right, and something more happens than just learning the values of classical bits? But all the Swap papers I have “browsed“ so far happily assumed that this is allowed. So I should be fine.

Still, this „poor man‘s“ teleportation is what forced me to come up with mental images of what happens, and strategies of how to argue/check whether they are right or wrong. Your „monogamy of entanglement“ argument was actually one part in my checking computation, that this „one single qubit in context can be encoded by two classical bits“ image works, or more precisely works at least in the context of Quantum teleportation (whether „poor man“ or not). (So far, I only checked the general case by decomposition into individual Quantum teleportations.)

Your post with that „dangerous way of thinking“ gave me the opportunity (or excuse) to present my image (single qubit „in context“), without also being forced to present my calculations and reasoning, or provide references to published papers detailing similar reaonings.

 

[vanhees71]

What has changed now is that I had the impression that your „monogamy of entanglement“ argument did convince PeterDonis. But I still couldn‘t see how it would change the things why I was unsure about the correct answer. Additionally, your „unconditional“ rejection of „locality“ raised for me the question, of how one could even argue in general (for or against anything), if decomposition into „local“ pieces is rejected.

Just my usual lamento: Please define, what you mean by "local" or "non-local". I still do not understand, how one can at the same time use QED to describe an experiment (here the entanglement swapping experiment) and at the same time deny that there are no causal connections possible between space-like separated events, and that's for me the only clearly defined meaning of "non-locality" there is.

In the textbook presentations and, as far as I understand it, also in the original paper by Bell locality is a much weaker assumtion, i.e., that the values (reality!) of the observables are determined once and for all by giving the values of the hidden variables in the very beginning, and that the measurement on B is not influenced by any manipulations/measurements on A and vice versa (locality!).

The difference to the local-QFT description is twofold: (a) the preparation does not determine the values of all observables but only the quantum state, which implies exclusively the probabilities for the possible outcomes of measurements on the so prepared system and (b) that locality is even stronger, i.e., that there cannot be any causal influence between spacelike separated events. Usually the argument for locality to be realized in experiments is even the assumption that there cannot be causal connections between spacelike separated events!

This gave me the idea to decompose the entanglement swapping experiment into two Quantum teleportations, and one Bell experiment:

In fact, the teleportations used for Swap are „poor man‘s“ teleportations, because they only use 1 out of the 4 possible measurement results (for each teleportation), and because there are two teleportations, only 1 out of 16 events is usable. (That‘s why I called it „poor man…“.) But there was another question for me, namely am I even allowed to assume that „poor man‘s“ teleportation still works, especially if I admit that you might be right, and something more happens than just learning the values of classical bits? But all the Swap papers I have “browsed“ so far happily assumed that this is allowed. So I should be fine.

I'd say entanglement swapping is one specific kind of teleportation. I don't understand, what you have doubts about: What's done in the final step is a coincidence measurement at three places: One measures the polarization of photon 1 at a place A, one does a coincidence measurement at place B on photons 2&3, which selects the events, where these states are found to be in the polarization-singlet state, which is especially easy to select, because it's the one state, where it's just sufficient that both detectors register a photon to be sure that the two photons are in this state, and a polarization measurement of photon 4 at place C. The measurements, i.e., the detection of the photons can be in any temporal order, and they can even be space-like separated, the outcome is always the same, i.e., that photon 1 and 4 are described also by the polarization-singlet Bell state. This, together with the assumption that micorcausality holds, and there's no reason to doubt this, because everything is described by standard QED, that there cannot be causal influences among the three (local!) measurements at the far-distant places A, B, and C. Although @DrChinese denies this again and again, it's a mathematical fact of standard QED!

Still, this „poor man‘s“ teleportation is what forced me to come up with mental images of what happens, and strategies of how to argue/check whether they are right or wrong. Your „monogamy of entanglement“ argument was actually one part in my checking computation, that this „one single qubit in context can be encoded by two classical bits“ image works, or more precisely works at least in the context of Quantum teleportation (whether „poor man“ or not). (So far, I only checked the general case by decomposition into individual Quantum teleportations.)

I've no clue, how you think you can describe a qubit with two classical bits at all. A qubit can be in a continuity of states, for two classical bits you have only 4 states. So how can there be a one-to-one connection between them?

Your post with that „dangerous way of thinking“ gave me the opportunity (or excuse) to present my image (single qubit „in context“), without also being forced to present my calculations and reasoning, or provide references to published papers detailing similar reaonings.

It's always better to talk in terms of formulae and calculations than in unclear everyday-language claims, which even contradict the mathematical facts about the theory (in this case QED) used to analyze the entanglement-swapping experiments.

 

[Simple question]

For each iteration (#i), you send randomly coloured pairs of socks [1&2] and [3&4] ...

Please read about Bell's theorem, which is not about Socks. Here is a good layman source
Spin do not work like colour, it is truly quatum. In your analogy the colour of the Socks will only match if both boxes are open at a the same angle. The trick is that the angle can be anything.

 

[Simple question]

2. I specifically meant it how I phrased it. The swap "causes" (where time ordering not relevant) the [1 & 2] monogamous entanglement to become [1 & 4] monogamous entanglement. [1 & 4] become a new quantum system (a biphoton). The state of [1] and [4] changed. Period.

I didn't meant to nitpick. But this rephrasing is perfect (bold's mine) because the sentence is complete and will not permit "local absolutist" to counter "A cannot change B" (which is also true). A (or B) can only change A and B.

 

[Simple question]

Just my usual lamento: Please define, what you mean by "local" or "non-local". I still do not understand, how one can at the same time use QED to describe an experiment (here the entanglement swapping experiment) and at the same time deny that there are no causal connections possible between space-like separated events, and that's for me the only clearly defined meaning of "non-locality" there is.

That's your usual straw-man, so I've fixed it.

The creation of correlation is space-like (even with only one pair), this has been measured and checked in the lab.

I think you cannot understand the issue of swapping because of your philosophy about "ensemble preparation" and micro-causality. It cannot be used to analyse the problem because the swapping of 2&3 is not in the past of either 1 or 4, so you cannot consider it as a valid "preparation procedure of ensemble".

There is no quibbles about what non-locality means.

 

[Simple question]

Sorry, I didn't follow the discussion so I don't know what is swapping network. Can you briefly explain it to me, or point to the post where this is clearly explained?

From DrChinese post #15, I understood that you can theoretically swap between as many "BSM" and kind a form a network. So event more complex number of "node" like this:

/\/\  /\/\/\
1234  123456

But more generally, the details of microscopic Bohmian trajectories are pretty much irrelevant. What matters are the macroscopic trajectories of pointers of the measuring apparatuses, for details see the paper linked in my signature.

But if all pointers follow the quantum potential evolution (trajectories or fields value), how can we determine the starting configuration of that field ? Is it theoretically possible ?
It intuitively seems to me that it would be more and more difficult to find one, the more you add nodes. Do you know if the Bohmian community have tackle this problem ?

 

[kurt101]

On the other hand, any interpretation in which nonlocal correlations are explained by reference to "updating" of our knowledge while retaining locality should, IMHO, be excluded as being ruled out by swapping experiments. Not all authors yet agree with me on this point, which is part of the reason I enjoy threads like this. Always looking for someone who has a strong counter-argument, but that hasn't happened yet. So far, hand-waving and not a shred of experimental support.

I gave you the best counter-argument I could think of. I submitted a program that obeys all of the relevant rules for the entanglement swapping experiment. The program demonstrates that the case where the BSM test is done on photons 2 & 3 after measuring 1 & 4 can be explained through causality. I can think of no better counter-argument then a program that simulates this experiment using hidden variables (short of a realistic theory that replaces quantum mechanics).

As far as I can determine the truth on this issue is that @DrChinese is correct that entanglement swapping does demonstrate non-locality, but only in the case where the BSM test done on photon's 2 & 3 is done before measuring 1 & 4. In the alternative case where the BSM test is done after it does not, which preserves causality. I kind of thought submitting the program would be enough to prove it, and put an end to this back and forth, but apparently not. I don't know if @DrChinese didn't read it (which I can understand), but if you are looking for a good counter argument I suggest that you do. And on top of that I also submitted a paper with the same position. So maybe you can tell me what else I can do to prove to you that the entanglement swapping experiment doesn't demonstrate a violation of causality and only demonstrates non-locality and is not so different than the EPR experiment in that respect.

 

[Demystifier]

But if all pointers follow the quantum potential evolution (trajectories or fields value), how can we determine the starting configuration of that field ? Is it theoretically possible ?
It intuitively seems to me that it would be more and more difficult to find one, the more you add nodes. Do you know if the Bohmian community have tackle this problem ?

In practice, we can't find the starting configuration. That's why, in practice, the Bohmian interpretation makes the same measurable predictions as standard QM.

 

[Simple question]

The program demonstrates that the case where the BSM test is done on photons 2 & 3 after measuring 1 & 4 can be explained through causality.

On this forum ? Can you provide a link to it ?

I can think of no better counter-argument then a program that simulates this experiment using hidden variables (short of a realistic theory that replaces quantum mechanics).

The argument would stand if the program could do both (before and after). Otherwise you've just assumed what you want to prove.

 

[martinbn]

In practice, we can't find the starting configuration. That's why, in practice, the Bohmian interpretation makes the same measurable predictions as standard QM.

Usually BM explains entangelment corations with some sort of action/influance between the particles. How does it work when, as in some swapping cases, the particles never existed at the same time!?

 

[vanhees71]

That's your usual straw-man, so I've fixed it.

The creation of correlation is space-like (even with only one pair), this has been measured and checked in the lab.

The creation of correlation is local: You create entangled photon pairs through local processes and then wait long enough for the photons to be detected (again each by a local measurement) at far distant places to detect the correlations described by entangled states. If the registration events of these photons are spacelike separated, due to the microcausality constraint fulfilled by QED, it is for sure not possible that a causal influence of one measurement on the other measurement causes the observered correlations, and indeed according to local relativsitic QFT the correlations are there from the very beginning, i.e., when preparing the entangled photon pair. That's not a straw-man but a mathematical feature of the theory successfully used to predict the outcome of these Bell tests.

I think you cannot understand the issue of swapping because of your philosophy about "ensemble preparation" and micro-causality. It cannot be used to analyse the problem because the swapping of 2&3 is not in the past of either 1 or 4, so you cannot consider it as a valid "preparation procedure of ensemble".

There is no quibbles about what non-locality means.

The swapping is achieved for a sub-ensemble of photon quadruplets measured in coincidence. That doesn't mean that the photons 1 and 4 are measured before or after or at space-like separation to the local measurement on photons 2 and 3, but that's precisely why I say that in such a setup it's impossible that the entanglement of 1&4 in this subensemble is caused by the local measurement on 2&3.

For me locality in connection with local relativistic QFT means that the microcausality constraint is fulfilled (by construction) and that thus there are no causal connections between space-like separated events possible.

If you now say that the phenomena prove non-locality you must mean something different, and I want to know, what you precisely mean by "locality" and thus by "non-locality".

What's often called "non-locality" is in fact "inseparability", i.e., the correlations between observables on long-distant entangled parts of a quantum system, but correlations don't imply causations.

 

[Fra]

Just to defend the subjective information route here..

There is no sense that QBism can describe perfect correlations of distant particles that have never been in contact as any form of "locality" or as being subjective in any way.

In they way I interpret things, the swapping is effectively a post selection of the outomes of the measurement at C (which needs to be communicated to D to work). I don't see the problem with this. Ontop of this the original "mystery" is I think present already in the original experiment without swapping.

This also explains why the causal order between C and D does not matter, except of course that the final conclusion at D can't happen until the measurent at C is done and communicated(by classical means) to D. Because the only "physical interaction" taking place between C and D, is communicating the C results required to post-select at D. Nothing else. This "communication" can in the experiment be "classical".

Sure, it may be non-realistic, but if so, there still needs to be an explanation of how the perfect correlations of distant particles arise.

To truly "explain this", beyond hand waving, one needs a new worked out theory (from the qbist stance). Which would within the accuracy of all known experiements give same predictions as QM, but maybe give more explanatory power and maybe include more interactions, but be constructed in away that provides much more insight on mechanisms in interactions.

I envision conceptually an "explanation" presumably in two parts

1) the correlation itself is explained by a kind of subjective hidden variable, that can not be cloned or copied like a classical variable, and this hidden variable does not imply the measurement results, it supposedly just explains the correlation. (effectively like QM does)

2) one needs in addition to explain why the above HV, does not obey bell inequality and thus doesnt behave as a ignorance HV. Not necessarily by loopholes, but by arguing that the anzats does not hold at all. Either one can come up with a competing theory to QM, and simply show it does not obey it (which is of course a huge task, and it will no longer be an innocent interpretation) or one can as a first step try to conceptually grasp general traits of such a theory and why the bell ansatz fails. This is ths hard part.

I'm not a bohmian but I do see similarities to the above and the solipsist HV. As subjective information of agents or particles are effectively the sort of solipsistic HV I imagine Demystifier entertains at times. If you see it this way, it wold not make sense to treat it as ignorance as it would imply that one observer/agent would try to average over somebody elses sample space, and that makes no sense.

No matter what else I disagree upon, I agree with this message

"Even if such HV's may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention."
-- https://arxiv.org/abs/1112.2034

I am possibly a bigger fan of these ideas than demystifier himself as it comes out of his mouth on only on his bad days, but it comes out of mine every day as I even find it philosophically appealing. So this thing seems like a common denominator of two very different ways of thinking. That two paths independently leads to the same thing is a good sign I think.

/Fredrik

 

[Demystifier]

Usually BM explains entangelment corations with some sort of action/influance between the particles. How does it work when, as in some swapping cases, the particles never existed at the same time!?

When particle creation is involved, then obviously non-relativistic QM, either in standard or Bohmian form, is not enough. So to answer your question, one must deal with Bohmian interpretation of relativistic QFT. There are several different versions of Bohmian QFT, so a precise answer depends on which version one uses. Perhaps the simplest version is the one which postulates an ontological existence of fields, rather than particles. In this version fields have some definite values at all times, everywhere in space, so the non-existence of particles is not a problem.

 

[kurt101]

On this forum ? Can you provide a link to it ?

The argument would stand if the program could do both (before and after). Otherwise you've just assumed what you want to prove.

I will send the program to you. I originally posted it in its own thread and Peter moved it to the thread Is Enanglement Swapping a result of post selection, or .. and then I think he deleted it as I don't see it there anymore. I think Peter deleted it with the reasoning that I was promoting my own theory, but it is not a theory just a toy model to prove DrChinese is misleading everyone in his conclusion. It demonstrates using math and logic what I am unable to communicate to @DrChinese in words.

@DrChinese seems to be the only one promoting the idea that entanglement swapping says more about interpretations than the EPR experiment. I think this forum needs to hold @DrChinese to the same standard everyone else is held to and ask him to provide a paper that support his views.

I see three independent sources that disagree with @DrChinese that use very different methodologies to reach that conclusion:

1. The program I wrote.
2. This paper https://link.springer.com/article/10.1007/s10701-021-00511-3#Sec21 which shares the same conclusion as my program.
3. The microcausality condition of QFT that @vanhees71 often brings up