Undergrad Murray Gell-Mann on Entanglement

[Demystifier]

I'll have a look at it. I take the publication in Nature as the final word on it, or is it rather v3 of the arXiv preprint the final word?

https://arxiv.org/abs/1111.3328

The publication in Nature and arXiv v3 are essentially the same. If there are any differences at all, they are not substantial.

 

[vanhees71]

I agree with you, but it seems to me that bringing up entanglement swapping just complicates things without adding any new feature. (Does it?)

Entanglement is a feature of the quantum state of a composite system. So asking whether entanglement is objective is a special case of asking whether the state is objective. The usual EPR experiment already raises that question. Initially, Bob's photon is described (by both Alice and Bob) as unpolarized, having the density matrix \frac{1}{2} |H\rangle \langle H| + \frac{1}{2} |V\rangle \langle V|. After Alice measures her photon, but before Bob finds out her result, Alice would describe Bob's photon as in the state |H\rangle \langle H|, while Bob would continue to use the unpolarized state.

Yes, and that's what's found in real-world experiments. If that was not the case, QT was wrong, which it is not according to the empirical facts. Bob will just see an ensemble of unpolarized photons. If, according to A's result, he looks only at the sub-ensemble where she found V for her photon, he'll find in all cases H. The choice of this sub-ensemble is, however only possible after A shared her result with B, and that takes at least the speed-of-light signal travel time to provide that information. This notion of states is, of course, purely epistemic. With an ontic meaning you'd run into the causality trouble and it would indeed be inconsistent since A associates another state than B, but in the ensemble interpretation the two states refer to different ensembles (either the whole ensemble if B didn't take notice of A's measurement or the partial ensemble where A measured V, and it's predicted that the 2nd ensemble has about only 1/2 the size as the 1st (full) ensemble).

Generally, I think physical theory is silent about ontics. It describes the outcome of observations/measurements but doesn't provide an "ontology". An electron is described in physics entirely by it's properties (mass, several charges of the standard model; in short it's a charged lepton with mass $m_e \simeq 0.511 \; \text{MeV}/c^2$), but the Standard Model doesn't tell you what it "really is" in any sense beyond these properties.

 

[stevendaryl]

Yes, and that's what's found in real-world experiments. If that was not the case, QT was wrong, which it is not according to the empirical facts. Bob will just see an ensemble of unpolarized photons.

Earlier, you were saying that by "state" you always mean something objective. But if Alice describes a photon as horizontally polarized, and Bob describes it as unpolarized, then either one of them is wrong, or the states are subjective.

[Note: you seem to be using ontic/epistemic for what I was calling objective/subjective]

 

[vanhees71]

Well, the conclusion of PBR is not that mysterious to me. What it really amounts to (I hope this isn't an oversimplification) is that if Alice and Bob use different pure states, |\phi\rangle and |\psi\rangle, say, to describe the same system, then one or the other (or both) of them is wrong. This is sort of obvious, because different states predict different probabilities. So if you can repeatedly place a system into the same state, then you can compile statistics that will rule out one state or the other. What PBR shows is that by using tensored states, you can distinguish between the two states in one measurement, so it's not necessary to compile statistics. That makes the conclusion more stark, but I don't find the conclusion itself very strange.

But as should be very clear, in the standard way of the ensemble interpretation as I've explained in several previous postings in this thread now, there is no contradiction between any probabilities. Using the definitions in my previous posting #182: Both Alice and Bob predict 50% V-polarized photons at Bob's place for the "full ensemble" and both Alice and Bob also predict 100% H-polarized photon for the subensemble, where Alice measured her photon to be V-polarized, supposed Bob is able to choose the subensemble based on Alice's information, which he can not get instantaneously but at most with a signal of the speed of light from Alice. So there is not contradiction whatsoever, it's only important to which preparation procedure/ensembles you refer to in subsequent measurements.

 

[vanhees71]

Earlier, you were saying that by "state" you always mean something objective. But if Alice describes a photon as horizontally polarized, and Bob describes it as unpolarized, then either one of them is wrong, or the states are subjective.

[Note: you seem to be using ontic/epistemic for what I was calling objective/subjective]

No, there is no contradiction between the association of states. You choose to look at either the full or a specific subensemble (see postings #182+#184). The association of the state for each of these ensembles is unambiguous (to use another word than objective/subjective now).

 

[stevendaryl]

No, there is no contradiction between the association of states. You choose to look at either the full or a specific subensemble (see postings #182+#184). The association of the state for each of these ensembles is unambiguous (to use another word than objective/subjective now).

You want to talk about ensembles, but an EPR experiment makes a prediction about single events: If (with correlated photons) Alice measures her photon to be horizontally polarized along an axis, then it is certain that Bob will measure his photon to be horizontally polarized along that axis.

 

[vanhees71]

You want to talk about ensembles, but an EPR experiment makes a prediction about single events: If (with correlated photons) Alice measures her photon to be horizontally polarized along an axis, then it is certain that Bob will measure his photon to be horizontally polarized along that axis.

Yes, and that's why Bob gets 100% H-polarized photons for the according subensemble. You cannot test the probabilistic predictions without ensembles. How else do you want to test it? If once you measure that Bob finds a H-polarized photon when Alice found her photon to be V-polarized (which of course you will for any single event in this situation) it doesn't tell you anything about whether the probabilistic prediction is right, but you have to repeat the experiment very often (also to get the desired minimal signficance level (like $5 \sigma$)).

 

[atyy]

The "collapse" as mere update is consistent with locality. But you open the possibility that collapse can be something more than that, in which case it is not consistent with locality. I think you confuse the readers by not always being explicit about which "collapse" do you have in mind.

By locality, vanhees71 means "locality of interactions". If we are in the minimal interpretation, the "locality of interactions" enforces no superluminal signalling. Collapse, whether physical or not, is consistent with locality of interactions for two reasons.

1) In the minimal interpretation, strictly speaking locality of interactions refers to the form of the Hamiltonian. The collapse (physical or not) does not affect the Hamiltonian, so collapse does not affect locality of interactions.

2) In the minimal interpretation, locality of interactions in the Hamiltonian enforces no superluminal signalling ("locality"). Collapse (physical or not) does not permit superluminal signalling, so collapse is consistent with locality.

3) For collapse to be inconsistent with locality, one must mean something more than locality in the minimal interpretation. One presumably means classical relativistic causality. I suspect that this is what vanhees71 means when he says collapse is inconsistent with locality of interactions - he must be taking the Hamiltonian to be real, and obeying classical relativistic causality. He may even be thinking of the action, which for a bosonic theory has the same form as classical relativistic theories. Collapse, taken to be physical, is certainly inconsistent with this form of locality. However, it is not correct to object to collapse for this reason, since Bell's theorem guarantess that classical relativistic causality is dead.

If vanhees71 were truly using a minimal interpretation, locality would have the meanings in (1) and (2). However, I believe he is using locality in the sense of (3), which means he is actually breaking from the minimal interpretation.

 

[stevendaryl]

Yes, and that's why Bob gets 100% H-polarized photons for the according subensemble. You cannot test the probabilistic predictions without ensembles.

If the prediction is that Alice and Bob will get the same result for the same polarization, then a single run is sufficient to falsify it. I think that bringing up ensembles is a red herring.

 

[vanhees71]

By locality, vanhees71 means "locality of interactions". If we are in the minimal interpretation, the "locality of interactions" enforces no superluminal signalling. Collapse, whether physical or not, is consistent with locality of interactions for two reasons.

1) In the minimal interpretation, strictly speaking locality of interactions refers to the form of the Hamiltonian. The collapse (physical or not) does not affect the Hamiltonian, so collapse does not affect locality of interactions.

2) In the minimal interpretation, locality of interactions in the Hamiltonian enforces no superluminal signalling ("locality"). Collapse (physical or not) does not permit superluminal signalling, so collapse is consistent with locality.

3) For collapse to be inconsistent with locality, one must mean something more than locality in the minimal interpretation. One presumably means classical relativistic causality. I suspect that this is what vanhees71 means when he says collapse is inconsistent with locality of interactions - he must be taking the Hamiltonian to be real, and obeying classical relativistic causality. He may even be thinking of the action, which for a bosonic theory has the same form as classical relativistic theories. Collapse, taken to be physical, is certainly inconsistent with this form of locality. However, it is not correct to object to collapse for this reason, since Bell's theorem guarantess that classical relativistic causality is dead.

If vanhees71 were truly using a minimal interpretation, locality would have the meanings in (1) and (2). However, I believe he is using locality in the sense of (3), which means he is actually breaking from the minimal interpretation.

Well, now it seems as if the difference in our opinion is rather whether you consider the interaction of the photon with the measurement device to be within relativistic QFT (which I do, just to be clear) or not. If you agree that this interaction is described within relativistic QFT anything physical "real" "ontic" that can happen in a causal sense must be due to local interactions between the photon and the measurement device.

If one disagrees with that (as do some flavors of the Copenhagen interpretation), and there are "two kinds of dynamics", i.e., a quantum dynamics described by the Hamiltonian and the dynamics describing interactions of measured systems with measurement devices, then indeed QT was incomplete as claimed by EPR.

I don't see any evidence in the literature that quantum-optical elements (like polarizers and photodetectors needed in the here discussed experiments) do not behave as expected when QED is applied.

 

[vanhees71]

If the prediction is that Alice and Bob will get the same result for the same polarization, then a single run is sufficient to falsify it. I think that bringing up ensembles is a red herring.

That's true. If you have perfect measurements, then a single contradiction is enough to disprove a prediction of a probability to be 100%, but a single agreement doesn't prove anything, and that's the point here!

 

[stevendaryl]

If one disagrees with that (as do some flavors of the Copenhagen interpretation), and there are "two kinds of dynamics", i.e., a quantum dynamics described by the Hamiltonian and the dynamics describing interactions of measured systems with measurement devices, then indeed QT was incomplete as claimed by EPR.

The hypothesis that there are these two kinds of dynamics is consistent with our observations. The alternative assumption that there is only one kind of dynamics, that described by the hamiltonian, may also be consistent with our observations, but it seems very complicated to actually demonstrate that. The interpretation that you seem to prefer seems operational indistinguishable from the 2-kinds approach, while your comments about locality seem to be about the 1-kind approach. If you are treating measurements as special (probabilities are only associated with measurement results, not with other kinds of interactions), then it seems to me that you're doing the 2-kinds approach.

 

[Demystifier]

Well, now it seems as if the difference in our opinion is rather whether you consider the interaction of the photon with the measurement device to be within relativistic QFT (which I do, just to be clear) or not. If you agree that this interaction is described within relativistic QFT anything physical "real" "ontic" that can happen in a causal sense must be due to local interactions between the photon and the measurement device.

If one disagrees with that (as do some flavors of the Copenhagen interpretation), and there are "two kinds of dynamics", i.e., a quantum dynamics described by the Hamiltonian and the dynamics describing interactions of measured systems with measurement devices, then indeed QT was incomplete as claimed by EPR.

I don't see any evidence in the literature that quantum-optical elements (like polarizers and photodetectors needed in the here discussed experiments) do not behave as expected when QED is applied.

I also believe that there are two kinds of dynamics. The standard quantum "Hamiltonian" dynamics governs the behaviour of ensembles, but it says almost nothing at the individual level. At the individual level, we need a different kind of dynamics. The Bell theorem implies that individual dynamics must be non-local.

The literature on quantum-optical elements concentrates on analysis of the ensemble properties, so it cannot see any evidence for individual dynamics. This is like trying to understand the dynamics of the ball in the roulette wheel by analyzing the statistics of ocurence of the numbers 0-36 in the roulette game.

 

[atyy]

Well, now it seems as if the difference in our opinion is rather whether you consider the interaction of the photon with the measurement device to be within relativistic QFT (which I do, just to be clear) or not. If you agree that this interaction is described within relativistic QFT anything physical "real" "ontic" that can happen in a causal sense must be due to local interactions between the photon and the measurement device.

If one disagrees with that (as do some flavors of the Copenhagen interpretation), and there are "two kinds of dynamics", i.e., a quantum dynamics described by the Hamiltonian and the dynamics describing interactions of measured systems with measurement devices, then indeed QT was incomplete as claimed by EPR.

I don't see any evidence in the literature that quantum-optical elements (like polarizers and photodetectors needed in the here discussed experiments) do not behave as expected when QED is applied.

Yes, I don't believe that the QM Hamiltonian describes the interaction between the quantum system and the measuring device. I use the "two kinds of dynamics" Copenhagen, which is what I call the minimal interpretation. This does not mean that polarizers or photodetectors are not described by QED. Rather it means that when we describe polarizers, then something else is the measuring device that measures the polarizer.

If you treat the interactions of QFT as physical or real or ontic, then won't you contradict the Bell theorem, which (roughly) says that reality is nonlocal?

Also, if you have a Hamiltonian for the whole universe, then won't you have a wave function of the universe?

 

[Simon Phoenix]

I agree with you, but it seems to me that bringing up entanglement swapping just complicates things without adding any new feature. (Does it?)

Yes, it's kind of a special case, I agree.

What I find interesting about the entanglement-swapping (and the GHZ projection) is that the projection is onto one of these 'holistic' states that Ken talks about. It's kind of interesting (well to me at least) that a local measurement can affect (apparently instantaneously) the physical properties (the entanglement) of two other objects that are remote from one another, and remote from the measurement. So it's not much of a 'new' feature, it's just a more interesting one to my mind than polarization.

It also calls into question, again in my mind, what it is we actually mean by entanglement. I really can't make a lot of sense out of the knowledge/information update approach to QM when it comes to entanglement. Our physical knowledge about something has to be described as some non-separable vector in a tensor product Hilbert space? What does that even mean? Yet we're happy to describe entanglement as a real, objective, property - and, curiously, this is actually reflected in the maths - but this maths doesn't represent anything physically real - just our state of knowledge? Don't buy it myself.

I confess that I'm kind of old-fashioned in my approach to QM - much happier thinking of the 'state' as at least partially descriptive of some real thing (with some possible subjective element) - measurements are done, the state collapses, all the usual. I do, however, recognize that this isn't entirely wonderful for a relativistically consistent interpretation though. So neither the much-derided ontic, or the epistemic interpretations make total sense to me.

I'm old-fashioned and prejudiced - what can I say?

 

[forcefield]

The Bell theorem implies that individual dynamics must be non-local.

Is it correct to say that order of measurement results here depend on measurement setting there ?

 

[ddd123]

Is the PBR theorem really relevant for MEI or similar? According to Scott Aaronson at least, it isn't: http://www.scottaaronson.com/papers/getreal.pdf

"if you adhere to the shut-up-and-calculate philosophy or the Copenhagen interpretation (which I think of as shut-up-and-calculate minus the shutting-up part) then the PBR result shouldn’t trouble you. You don’t have an ontology: you consider it uninteresting or unscientific to discuss reality before measurement. For you, ψ is indeed an encoding of human knowledge, but it’s merely knowledge about the probabilities of various measurement outcomes, not about the state of the world before someone measures."

The theorem supposedly only attacks the psi-epistemic WITH underlying ontology camps.

 

[ddd123]

If we think of connectivity of space as important for concepts like nonlocality, and if we interpret entanglement as fundamentally an issue about the holism of systems, then the article seems to be suggesting that our discussion about nonlocality vs. holism has an interesting duality as well: nonlocality in the bulk is dual to holism on the boundary. Put differently, the idea in the article is that the space in the bulk is in some sense "due to" entanglement on the boundary, such that space is "made of entanglement", as they like to say.

I don't suppose you have any idea why long-range correlations would play a role in keeping space connected? That sort of maths is just too advanced for me.

But anyway I like this idea that holism is the default, and phenomenological separability means that something has gone wrong and we have to figure out why.

 

[calinvass]

Quantum entanglement is empiricaly demonstrated to be real. However we can never be absolutely sure. I guess anyone is invited to prove it wrong. Somewere might be an error or a different mechanism, but that is extremely unlikely.
Any demonstration must be logical, and this one it is. The problem is that the consequences are ridiculous or extremely hard to believe, but it doesn't mean they can't be correct.
For example, instant coordination between particles can suggest a different dimension for the wave function and aloso shared wave function.
Consciousness collapsing a wave function is way more ridiculous, very close to illogical.

 

[Ken G]

I don't suppose you have any idea why long-range correlations would play a role in keeping space connected? That sort of maths is just too advanced for me.

The math is apparently "tensor networks", which I know nothing about but I'm guessing its' 5 years of study before you have a clue.

But anyway I like this idea that holism is the default, and phenomenological separability means that something has gone wrong and we have to figure out why.

Yes, I like that too, so I appreciate our discussion to help bring this out.

 

[atyy]

The math is apparently "tensor networks", which I know nothing about but I'm guessing its' 5 years of study before you have a clue.

If you know QM, it's about 5 seconds of study.

Tensor networks are basically a pictorial representation of the entanglement structure of a wave function. The pictorial representation of a wave function is similar in spirit to the Penrose pictorial representation of tensors.

Appropriately, some of the tensor networks look like curved space. An important point going beyond looks is that calculations using tensor networks approximate a formula called the Ryu-Takayangi formula with the same form as the Hawking formula - which relates the entropy of entanglement to the entropy of a region of space.

 

[vanhees71]

Yes, I don't believe that the QM Hamiltonian describes the interaction between the quantum system and the measuring device. I use the "two kinds of dynamics" Copenhagen, which is what I call the minimal interpretation. This does not mean that polarizers or photodetectors are not described by QED. Rather it means that when we describe polarizers, then something else is the measuring device that measures the polarizer.

If you treat the interactions of QFT as physical or real or ontic, then won't you contradict the Bell theorem, which (roughly) says that reality is nonlocal?

Also, if you have a Hamiltonian for the whole universe, then won't you have a wave function of the universe?

Where is the evidence that the various devices used to detect and manipulate photons do not obey the standard natural laws as described by (many-body) relativistic QFT. I don't have any example, where such a deviation from the "Standard Model" is observed.

All our physical theories don't provide "ontic" pictures. They are descriptions of the behavior of observable properties of "real objects" in nature.

 

[Demystifier]

Is the PBR theorem really relevant for MEI or similar?

The theorem supposedly only attacks the psi-epistemic WITH underlying ontology camps.

You are right that PBR is not a problem for interpretations that deny ontology. But MEI, in my understanding, does not deny ontology. MEI is rather agnostic about ontology. By agnostic, I mean - "Yeah, ontology might exist, but I don't care what it is as long as I can't explicitly measure it".

 

[vanhees71]

The publication in Nature and arXiv v3 are essentially the same. If there are any differences at all, they are not substantial.

Yesterday night I had a first look on the paper. I don't understand the ansatz in the beginning. The authors seem to imply that if the quantum state, described by a statistical operator (or for the special case of pure states by a ray/representing state ket in Hilbert space), is interpreted as the mere knowledge of the observer about a system, there must be an underlying "more comprehensive state description", labeled as $\lambda$, which has a probability distribution $\mu(\lambda)$. Isn't this nothing else than the "hidden variable aproach"?

For me the current status of QT rather suggests that there is no such thing as a deterministic underlying state description but QT tells us what we can possibly know about the system. In other words for the example for a spin/angular momentum you can make $\vec{j}^2$ and one component, usually $j_z$, determined. All the other components of the angular momentum, $j_x$ and $j_y$, are then indetermined, and there is no hidden variable or anything else that in fact determines their values.

 

[Demystifier]

All our physical theories don't provide "ontic" pictures. They are descriptions of the behavior of observable properties of "real objects" in nature.

Classical mechanics says that the Sun is there even during the night. That's quite ontic to me.

 

[vanhees71]

QT also says that the sun is there even during the night. It's observable just at another place on Earth ;-)).

 

[Demystifier]

QT also says that the sun is there even during the night. It's observable just at another place on Earth ;-)).

No, because on that other place it is not night.

 

[ShayanJ]

Isn't this nothing else than the "hidden variable aproach"?

They're not assuming that a hidden variables approach is correct. They're just examining what such an approach implies in their case and compare it with approaches that assume the quantum state is the objective state. As far as I understand, none of them is your point of view, because you seem to assume the quantum state as subjective but at the same time don't assume any underlying theory that gives an objective state.

 

[Demystifier]

Yesterday night I had a first look on the paper. I don't understand the ansatz in the beginning. The authors seem to imply that if the quantum state, described by a statistical operator (or for the special case of pure states by a ray/representing state ket in Hilbert space), is interpreted as the mere knowledge of the observer about a system, there must be an underlying "more comprehensive state description", labeled as $\lambda$, which has a probability distribution $\mu(\lambda)$. Isn't this nothing else than the "hidden variable aproach"?

Yes, it is a hidden-variable approach.

For me the current status of QT rather suggests that there is no such thing as a deterministic underlying state description but QT tells us what we can possibly know about the system. In other words for the example for a spin/angular momentum you can make $\vec{j}^2$ and one component, usually $j_z$, determined. All the other components of the angular momentum, $j_x$ and $j_y$, are then indetermined, and there is no hidden variable or anything else that in fact determines their values.

It is not clear to me what do you mean by "deterministic" and "determined". Is it the opposite to truly random? Or is it the opposite to existing only when measured? The difference is very important because there are models with stochastic (i.e. truly random) hidden variables, which also need to be non-local by the Bell theorem.

 

[atyy]

Where is the evidence that the various devices used to detect and manipulate photons do not obey the standard natural laws as described by (many-body) relativistic QFT. I don't have any example, where such a deviation from the "Standard Model" is observed.

All our physical theories don't provide "ontic" pictures. They are descriptions of the behavior of observable properties of "real objects" in nature.

Standard QFT requires a Heisenberg cut. This does not mean that any system does not obey QT. It simply means that QT cannot describe the whole universe (unless you have Bohmian Mechanics or MWI).

If you believe there is a Hamiltonian of the universe, then doesn't that mean that you believe there is a wave function of the universe?