# Bell-state entanglement swapping and retrocausality

entropy1

In this article of Anton Zeilinger et al. they perform an experiment which suggests FTL or retrocausal influence.

Alice and Bob both produce their own polarisation-entangled photon pair, both send one photon of the pair to Victor, and measure the polarisation of the other themselves. Victor performs one of two measurements of the photons he receives from Alice and Bob: a separate measurement, or a Bell state measurement, the latter of which has the effect of entangling the photons, which causes entanglement swapping, thus entangling the photons Alice and Bob measure. Victor measures after Alice and Bob have measured their photons.

As I understand it, when Victor makes a separate measurement, after investigation Alice's and Bob's photons are not correlated, and when Victor makes a Bell-state measurement, thus entangling Alices's and Bob's photons, those photons are correlated after investigation.

Now, I understand that strictly speaking this does not imply retrocausality or FTL influence. But the fact that Victor's decision to make a Bell-state measurement or a separate measurement determines whether Alice's and Bob's measurements are correlated, while being done prior to Victor's decision makes me wonder! For how to explain that Alice's and Bob's photons are correlated, if not for the fact that Victor is going to make a Bell-state measurement? There is in my eyes no reason for a strict correlation between Alice and Bob other than a future decision by Victor! In my eyes this suggests retrocausality! Is this really possible?

Gold Member
In this article of Anton Zeilinger et al. they perform an experiment which suggests FTL or retrocausal influence.
Your link seems wrong. It gives loophole free electron Bell test experiment.

Now, I understand that strictly speaking this does not imply retrocausality or FTL influence. But the fact that Victor's decision to make a Bell-state measurement or a separate measurement determines whether Alice's and Bob's measurements are correlated, while being done prior to Victor's decision makes me wonder! For how to explain that Alice's and Bob's photons are correlated, if not for the fact that Victor is going to make a Bell-state measurement? There is in my eyes no reason for a strict correlation between Alice and Bob other than a future decision by Victor! In my eyes this suggests retrocausality! Is this really possible?
There is important detail about the experiment. Bell-state measurement splits Alice's and Bob's measurements into subsamples and within these subsamples Alice's and Bob's measurements are correlated.

Ilja
There is no retrocausality, because it all fits into standard quantum theory. And for standard quantum theory, we have a non-local but causal hidden variable theory, without retrocausality, but with normal causality following the absolute time t of the Schroedinger equation. This is the de Broglie-Bohm interpretation.

In such experiments, what confuses is that people tend to think about causality in terms of Einstein causality. Once an explanation in terms of Einstein causality fails, they are in horror, and ready to accept whatever else comes to mind, including things like retrocausality. Some prefer to give up causality completely instead of giving up the nice idea that relativistic symmetry is something fundamental: A Lorentz-invariant retrocausality seems more natural to them when a classical causal world with a hidden preferred frame which violates Lorentz-invariance.

entropy1
Your link seems wrong. It gives loophole free electron Bell test experiment.

I'm sorry; The link is correct, but I should mention that there are in fact electrons involved.

There is important detail about the experiment. Bell-state measurement splits Alice's and Bob's measurements into subsamples and within these subsamples Alice's and Bob's measurements are correlated.

I'm trying to understand on the basic level; How can Alice's and Bob's measurements be split if they only measure polarisation (once)?

Gold Member
I'm sorry; The link is correct, but I should mention that there are in fact electrons involved.
and no Zeilinger involved.

I'm trying to understand on the basic level; How can Alice's and Bob's measurements be split if they only measure polarisation (once)?
There are four different theoretical outcomes for Victor's Bell-state measurement. So based on Victor's measurement outcome you split Alice's and Bob's measurements into subsets (after you bring together measurements from all three parties).

entropy1
and no Zeilinger involved.

You're entirely right! Sorry for that!

There are four different theoretical outcomes for Victor's Bell-state measurement. So based on Victor's measurement outcome you split Alice's and Bob's measurements into subsets (after you bring together measurements from all three parties).

So far I think I understand. Does that mean that the manner in which Alice's and Bob's photons (electrons) correlate can differ in four different ways?

Gold Member
Does that mean that the manner in which Alice's and Bob's photons correlate can differ in four different ways?
Yes. They can be correlated or anticorrelated in H/V basis and correlated or anticorrelated in +45 deg./-45 deg. basis. That makes 4 combinations.

entropy1
Yes. They can be correlated or anticorrelated in H/V basis and correlated or anticorrelated in +45 deg./-45 deg. basis. That makes 4 combinations.

To be clear: are we talking about the measurements Alice and Bob are taking?

StevieTNZ
I am assuming you are referring to this experiment: http://www.nature.com/nphys/journal/v8/n6/full/nphys2294.html If so, these are my own thoughts on the experiment (I've had much correspondence with Johannes Kofler and Xiao-song Ma [as well as Caslav Brukner]):

I actually suspect, and this follows from QM formalism, that when Alice and Bob 'measure' their photons, all that happens is entanglement between the photon and the detector. No collapse of the wave function occurs. Johannes Kofler was kind enough to send me a Mathematica file that showed the evolution of the photons through the interferometer in the delayed choice entanglement swapping experiment.

The bell-state HH-VV was observed if at Victor's end certain detectors were set off. The measurement basis of Alice and Bob's photons was in the 45/135 basis. To measure in this basis wave plates and PBS orientated in the H/V basis were used. To infer one photon was |45> and the other |135> one would need to observe, if Alice and Bob's photons were in the bell-state HH-VV, |H>(Alice)|V>(Bob) or |V>(Alice)|H>(Bob). If they assumed these definite polarization at detection before Victor's measurement, the other photons entering the interferometer would be |H> and |V> polarized. This leads, however, to a separable state (i.e. it cannot lead to either the bell state HH+VV or HH-VV).

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entropy1
How do I interpret:
$$\mid 0> _{A} \otimes \mid 0> _{B}$$
or HH?

StevieTNZ
How do I interpret:
$$\mid 0> _{A} \otimes \mid 0> _{B}$$
or HH?
I was lazy, but it should read |H>|H> - |V>|V>, which means two photons are entangled. If you measure one and get horizontal (|H>) as the polarization, then the other photon will be found also in the horizontal polarization.

Likewise if you have entangled photons in the bell state |H>|V> - |V>|H>, and you measure one and find it to be |H> the other will be found vertically polarized |V>.

Gold Member
To be clear: are we talking about the measurements Alice and Bob are taking?
We are talking about potential measurements Alice and Bob can take or description of Alice's and Bob's electrons (or photons).
Real measurements can't happen in two different bases (probably that's why you are asking that question).

entropy1
To be clear: are we talking about the measurements Alice and Bob are taking?

Yes. They can be correlated or anticorrelated in H/V basis and correlated or anticorrelated in +45 deg./-45 deg. basis. That makes 4 combinations.

We are talking about potential measurements Alice and Bob can take or description of Alice's and Bob's electrons (or photons).
Real measurements can't happen in two different bases (probably that's why you are asking that question).

I don't understand entirely. The outcome of the measurements by Victor is one out of four possibilities, and the outcome by Alice and Bob jointly is one out of four possibilities? As far as I can tell the only results are that after the Bell-measurement Victor's photons become entangled, and, independently in measured value, Alice's and Bob's photons become entangled?

I am suspecting that there are more ways to be entangled than just anti-correlation...

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Gold Member
There is in my eyes no reason for a strict correlation between Alice and Bob other than a future decision by Victor! In my eyes this suggests retrocausality! Is this really possible?

A great one by Zeilinger's group:

http://arxiv.org/abs/quant-ph/0201134

Although these type of experiments are suggestive of retrocausality, they are not considered proof. Each so-called interpretation of Quantum Mechanics explains this in its own manner. There are also interpretations in which the future is a factor in outcome statistics.

Gold Member
2022 Award
It should be "explained" using QED, and this tells us (by construction of the theory) that everything is causal, and interactions are local, particularly also the detection of a photon in a photodetector is local. Consequently, there is no spooky action at a distance involved, but there can be correlations between parts of a quantum system measurable by observers which are a far distance away from each other, as in the typical teleportation setup in experiments like the Zeilinger experiment in the quoted paper.

In my opinion this is independent of any specific interpretation of quantum theory. It just uses as much interpretation as you need to describe nature in terms of the mathematical abstractions of quantum theory. Anything going beyond this minimal statistical interpretation is metaphysics and thus not subject of this discussion!

entropy1
It should be "explained" using QED, and this tells us (by construction of the theory) that everything is causal, and interactions are local, particularly also the detection of a photon in a photodetector is local. Consequently, there is no spooky action at a distance involved, but there can be correlations between parts of a quantum system measurable by observers which are a far distance away from each other,

Is it fair if I throw in the term 'decoherence'? In the end, all information must come together to draw conclusions, and that is in fact a result of decoherence... does that view make any sense?

Gold Member
I don't understand entirely. The outcome of the measurements by Victor is one out of four possibilities, and the outcome by Alice and Bob jointly is one out of four possibilities? As far as I can tell the only results are that after the Bell-measurement Victor's photons become entangled, and, independently in measured value, Alice's and Bob's photons become entangled?
From Victor's measurement you find out what type of correlation is between Alice's and Bob's photons.
Let me give simple analogy. Say you have string consisting of ones and zeros. Then Victor tells you how to split that string in two substrings (which number in sequence goes into which subset). After you do that you find that all ones end up in one subset and all zeros in other. In that case you won't claim that Victor retrocausally changed values in your string, right?
So the case where Victor's measurements happen after Alice's and Bob's measurements is consistent with such kind of explanation.
However it won't work if Alice's and Bob's measurements are performed after Victor's measurement (because of Bell inequalities). But this is just a side note as we are not discussing that type of setup.

Gold Member
2022 Award
Is it fair if I throw in the term 'decoherence'? In the end, all information must come together to draw conclusions, and that is in fact a result of decoherence... does that view make any sense?
Indeed, decoherence is important here, because for the measurements of this kind to be possible, the measurement must store irreversibly the information of its outcome somehow. Alice and Bob must take a measurement protocol, carefully noting the time of their detection events, so that they can compare the outcome of their individual measurements making sure that they can check for the "Bell correlations" of the entangled pairs, i.e., they must be sure after the measurement which detection event at A is due to one photon of an entangled pair, of which the 2nd photon has been measured at B.

Another point is to make oneself clear, what's meant by "retorcauslity" here. It's of course nothing retrocausal. The only point is that using an appropriate measurement protocol you can choose different subensembles of the total ensemble of measurement events. A very fascinating example is the now famous quantum erasure experiment,

https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

The expression "delayed choice" is much better than to envoke "retrocausality", because nothing is "retrocausally" changed about the measured photons or the measurement setup after the measurement is done. To the contrary one uses fixed measurement protocols to choose different subenensembles after the experiment was finished. The one ensemble contains (full or partial) which-way information, while the other demonstrates (partial or full) quantum interference by measuring an interference pattern. The latter is the better, i.e., has the more contrast, the fewer which-way information is given by the chosen subensemble and vice versa. So "delayed choice" (of the ensemble) is a way more accurate terminology than calling it "retrocausality".

entropy1
Thanks for the two previous answers. Judging from the delayed choice quantum eraser experiment it seems to me that the correlation (interference pattern) is due to ('caused by') the particle-wave duality of photons. Is that also the case in the experiments we are talking about in this topic?

Second question: if there is no causality in principle, does that mean that the correlations between the measurements (the outcomes of the measurements) are completely beyond the experimenter's control in this case?

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Gold Member
2022 Award
First of all there is no wave-particle duality. This is an old concept, and nothing is farther from the notion of classical particles than photons! I cannot find the time at the moment to finish my Insight article on photons. It's not a simple concept, but it's much simpler to learn it right than using olf-fashioned misleading ideas. Photons are special states (Fock states, i.e., states with a determined photon number) of the free electromagnetic field. It is not even possible to define a position of a single photon as you can for massive particles (or particles with spin ##s \leq 1/2##). The correlation is described by the local relatististic quantum field theory, named QED (quantum electrodynamics), no more no less. There is no other way to understand photons than to learn QFT, but that's great fun!

Causality is the fundamental principle, without which no natural sciences was possible at all. If there are no natural laws, you cannot do natural science as we understand it, and all of fundamental physics so far is causal, starting from the space-time structure, underlying all physics (classical and quantum).

The correlations we are talking about cannot be described other than with quantum theory, i.e., today we do not have any other theory that can describe them. The correlations are in astonishing control of the expermenter nowadays. Quantum opticians can prepare polarization-entangled photons with great certainty, using parametric downconversion, where you shoot a laser beam into certain berefringent chrystals and get out polarization-entangled two-photon Fock states. These state preparations are among the most precisely possible ever!

This, however also implies that the single photons have totally indetermined polarization. It is not a technical problem of measurement that makes these observables uncertain or hard to measure, but the single photons in the entangled two-photon state really do not have determined polarizations. This is the inherent probabilistic nature of quantum theory, and more and more and ever more precise measurements indicate that it is also an inherent property of nature itself, not only of the theory describing it.

entropy1
This, however also implies that the single photons have totally indetermined polarization. It is not a technical problem of measurement that makes these observables uncertain or hard to measure, but the single photons in the entangled two-photon state really do not have determined polarizations. This is the inherent probabilistic nature of quantum theory, and more and more and ever more precise measurements indicate that it is also an inherent property of nature itself, not only of the theory describing it.

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Staff Emeritus
This, however also implies that the single photons have totally indetermined polarization. It is not a technical problem of measurement that makes these observables uncertain or hard to measure, but the single photons in the entangled two-photon state really do not have determined polarizations.

But after someone measures the polarization of one of the photons, the other photon DOES have a definite polarization, right?

Heinera
But after someone measures the polarization of one of the photons, the other photon DOES have a definite polarization, right?
Well, it's not as simple as that since which measurement is before and which is after depends on the observer (frame dependent).

Gold Member
Well, it's not as simple as that since which measurement is before and which is after depends on the observer (frame dependent).
Measurements can be timelike separated and then it's simple.

Mentor
Measurements can be timelike separated and then it's simple.

The timelike-separated case can be made simple in this manner, but the price is steep: by accepting a explanation that only works for the timelike-separated case, we are compelled to find some completely different explanation to apply in the spacelike-separated case. Thinking of the two cases as fundamentally different seems ugly to me. This ugliness is not reduced by considering that given an event E1 I can always find events E2 and E3 such that the spacetime interval between E2 and E3 can be made arbitrarily small, yet E1 and and E2 are timelike-separated and E1 and E3 are spacelike-separated; it feels wrong that the correct understanding of an experimental setup might change because I move a detector one micron to the left.

The first Bell-type experiments were done with time-like separations. Although everyone recognized the necessity of closing the resulting loophole, the willingness to do these experiments despite the loophole suggests a general belief that the correlations in the timelike and spacelike cases should have a common explanation.

Heinera