Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

[Greg Bernhardt]

TL;DR Summary

Entangled photons violate the Bell-CHSH inequality because quantum mechanics gives discrete pass/fail outcomes rather than smooth classical averages. Their correlations exceed what any hidden-variable theory allows, reaching the maximum quantum limit and revealing nonlocal behavior. - ChatGPT5

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles.

In her YouTube video Bell’s Theorem Experiments on Entangled Photons, Dr. Fugate shows how polarization-entangled photons violate Bell’s inequality. In this Insight, I will use quantum information theory to explain why such entangled photon-polarization qubits violate the version of Bell’s inequality due to John Clauser, Michael Horne, Abner Shimony, and Richard Holt known as the Clauser-Horne-Shimony-Holt (CHSH) inequality...

Source: https://www.physicsforums.com/insig...ls-inequality-per-quantum-information-theory/

written by @RUTA

 

[RUTA]

Who wrote that summary? It's spot on, yet concise. I've presented this idea more generally at conferences and seminars around the world and published it in a book, papers and blogs, but whoever wrote this summary did a better job :-)

 

[Greg Bernhardt]

Who wrote that summary?

ChatGPT5

 

[RUTA]

ChatGPT5

Damn, beat by a bot

 

[Greg Bernhardt]

Damn, beat by a bot

Hey, summarization is actually one thing it's qualified to do

 

[RUTA]

Would you mind moving the link to this Insight to the Quantum Interpretations and Foundations Forum?

 

[PeterDonis]

Would you mind moving the link to this Insight to the Quantum Interpretations and Foundations Forum?

As far as I can see, the things being discussed are independent of any interpretation; they're experimental facts and how the predictions of them are derived from the math of QM.

 

[RUTA]

As far as I can see, the things being discussed are independent of any interpretation; they're experimental facts and how the predictions of them are derived from the math of QM.

Well, I hope one day that introductory physics textbooks will contain our particular completion of the quantum reconstruction of Hilbert space like they do Einstein's reconstruction of the Lorentz transformations. The two are exactly analogous and based on the relativity principle, but as of now there are still some in quantum information theory who do not like our "interpretation of the quantum reconstruction program" even while they admit its beautiful parallel with special relativity. As you'll note, I do rely on our completion to derive the joint probabilities for the entangled photon-polarization qubits, so it could be considered more appropriate for the Interpretations forum, but I'll leave that up to you :-)

 

[PeterDonis]

our particular completion of the quantum reconstruction of Hilbert space

Ah, I see, by "quantum information theory" you meant your particular interpretation of where the standard QM predictions come from. In that case, I would agree this belongs in the interpretations subforum.

I think "quantum information theory" might be a misleading term for it, since to me that connotes the sorts of things one sees in quantum computing, i.e., more an "engineering" thing (what quantum gates do I use?) than a foundations thing. But I might be unfamiliar with the terminology in this area.

 

[PeterDonis]

In that case, I would agree this belongs in the interpretations subforum.

And I have now moved it there.

 

[gentzen]

And I have now moved it there.

The red Insights tag in the thread title is gone now.

 

[PeterDonis]

The red Insights tag in the thread title is gone now.

Hm, that's odd, it's not showing up as a title tag option any more.

@Greg Bernhardt is that something peculiar to the QM interpretations subforum? Can it be fixed?

 

[gentzen]

our particular completion of the quantum reconstruction of Hilbert space like they do Einstein's reconstruction of the Lorentz transformations. The two are exactly analogous and based on the relativity principle

If they were exactly analogous, you should also be able to spell out what corresponds to "relativity of simultaneity" in the case of QM, not just what corresponds to the "observer independence of the speed of light".

And whatever that should turn out to be, I fear it will be just as counter-intuitive as "relativity of simultaneity", if not more. One counter-intuitive property of QM in Everett's interpretation is that the past is only real in as far as there are still records of that past in the present.

In the simulation of the interaction of electrons with a sample in a scanning electron microscope, I can see very concrete in action how that works: If the electron passes close by an atom, but doesn't manage to cause a lasting effect by ejecting an electron or transmitting momentum to the nucleus (or ...), then it is the same for the electron as if that close encounter would never have happened.

 

[PeterDonis]

One counter-intuitive property of QM in Everett's interpretation is that the past is only real in as far as there are still records of that past in the present.

I'm not sure what you mean by this. In the MWI, "worlds" split when decoherence occurs, and decoherence is much broader than "records". And once worlds split, they don't recombine, so the decoherence doesn't get undone. So whatever "past" is embodied in the current world you're in isn't going to change.

 

[gentzen]

In the MWI, "worlds" split when decoherence occurs, and decoherence is much broader than "records".

In Everett's thesis, he analyses the predictions of QM based on the information available to the agent which tries to verify them. In the decoherent histories literature, that concept from Everett continues its life as the concept of Information Gathering and Using System (IGUS).

The thing with "worlds" which split is less easy to find in Everett's thesis. It certainly is there too, but not so direct and openly visible as in Bryce deWitt's account of Everett's discovery.

 

[PeterDonis]

In Everett's thesis, he analyses the predictions of QM based on the information available to the agent which tries to verify them....

The thing with "worlds" which split is less easy to find in Everett's thesis.

Yes, I agree. But I still don't understand what you mean by what I quoted from you in post #14.

 

[RUTA]

Ah, I see, by "quantum information theory" you meant your particular interpretation of where the standard QM predictions come from. In that case, I would agree this belongs in the interpretations subforum.

I think "quantum information theory" might be a misleading term for it, since to me that connotes the sorts of things one sees in quantum computing, i.e., more an "engineering" thing (what quantum gates do I use?) than a foundations thing. But I might be unfamiliar with the terminology in this area.

Quantum computing, quantum cryptography, and the reconstruction of quantum mechanics via information-theoretic principles are programs in quantum information theory and the "second quantum revolution." The first two programs get far more attention than the third for obvious reasons.

According to Goyal (2024), the elucidation of quantum mechanics via its reconstruction is a two-step process: "Reconstruct the formalism" then "Interpret the reconstruction." If one was only "interpreting" an information-theoretic reconstruction (nothing added), then that would be equivalent to the "interpretations program" a la dBB and Many-Worlds because as Van Camp notes, "nothing additional has been shown to be incorporated into an information-theoretic reformulation of quantum mechanics beyond what is contained in quantum mechanics itself." However, we've done more than that.

First, we show that Information Invariance & Continuity (essentially just an information-theoretic way to characterize qubit superposition) entails the observer-independence of h under spatial rotations and translations. That is certainly an "interpretation" of those reconstructions based on Information Invariance & Continuity, since this requires the spatialization of measurement that most information approaches pride themselves on avoiding. Based on that "interpretation" it is then obvious that Information Invariance & Continuity can be justified by the relativity principle and Planck's radiation law, just like the light postulate is justified by the relativity principle and Maxwell's equations. Strictly speaking, we have then added something to quantum mechanics, i.e., the relativity principle. That's why we have a "completion" of the quantum reconstruction program based on our "interpretation" of Information Invariance & Continuity.

Hope this helps clarify the classification of our work :-)

 

[PeterDonis]

Hope this helps clarify the classification of our work :-)

Yes, it does, thanks!

 

[RUTA]

If they were exactly analogous, you should also be able to spell out what corresponds to "relativity of simultaneity" in the case of QM, not just what corresponds to the "observer independence of the speed of light".

And whatever that should turn out to be, I fear it will be just as counter-intuitive as "relativity of simultaneity", if not more.

You are correct, there is a counterintuitive consequence of the observer-independence of h corresponding to the relativity of simultaneity, i.e., the counterintuitive consequence of the observer-independence of c. The relativity of simultaneity represents a change in our view of Newtonian space and time to Minkowskian spacetime. The corresponding counterintuitive consequence of the observer-independence of h is qubit superposition. Accordingly, what we expect from measurements per classical physics holds only on average per qubit superposition, i.e., 'average-only' projection of angular momentum for the spin-1/2 qubit (Newtonian mechanics) and 'average-only' transmission of energy for the photon-polarization qubit (electromagnetism).

Edit: I think many (most?) physicists would not be surprised that qubit superposition outcomes are just what happens when you try to relate discrete results of a fixed minimum size to the corresponding continuous classical case. However, when you entangle qubits to represent conservation per the corresponding classical case, your 'average-only' projection/transmission leads to 'average-only' conservation characterizing the mystery of Bell state entanglement.

 

[gentzen]

Yes, I agree. But I still don't understand what you mean by what I quoted from you in post #14.

You quoted:

One counter-intuitive property of QM in Everett's interpretation is that the past is only real in as far as there are still records of that past in the present.

I mean the property of QM first emphasized by Everett, to which Bohmians will point, if Arnold Neumaier or Robert Helling claim that Bohmian mechanics would make wrong predictions for multi-time correlations. Even non-Bohmians will happily point to that property:

Ah, but what about multi-time correlations? As soon as we’re talking about the wave function of the entire universe, it becomes obvious that multi-time correlations are not directly observable in QM. What’s observable is only, e.g., the correlation between the position of a particle at time t₂, and your record of where the particle was when you measured it at an earlier time t₁. But to measure the particle you needed to interact with it, and then we’re again just talking about the standard Born rule, and the Bohmians will make the same predictions as everyone else.

 

[PeterDonis]

I mean the property of QM first emphasized by Everett, to which Bohmians will point, if Arnold Neumaier or Robert Helling claim that Bohmian mechanics would make wrong predictions for multi-time correlations.

This isn't saying that the past isn't real unless we have records of it. It's only saying that we can't evaluate predictions about multi-time correlations except by comparing present observations with records of past ones, so if we don't have such records, we can't make the comparison. But that's a much, much weaker claim than the claim that the past isn't real unless we have records of it.

 

[PeterDonis]

Even non-Bohmians will happily point to that property:

The same "property" would apply to correlations between observations made at the same time at different places--for example, in any test of Bell inequality violations. "Directly observable", in the sense Aaronson is using the term in that quote, is an extremely narrow property, and practically no prediction of any interest in physics is "directly observable" in this sense. So I'm underwhelmed by any claims based on a prediction not being "directly observable".

 

[gentzen]

So I'm underwhelmed by any claims based on a prediction not being "directly observable".

I'm not convinced that "relativity of simultaneity" is based on much stronger grounds. Maybe the microwave background defines a preferred reference frame, and hence simultaneity is actually absolute. But the observable simultaneity will depend on how clocks are synchronized, and that synchronization is what determines observable lengths, and observable time differences at different places (i.e. when a particle passes at two places at different times, and each place records the exact time when the particle passed).

 

[PeterDonis]

I'm not convinced that "relativity of simultaneity" is based on much stronger grounds.

It's a necessary implication of relativity.

Maybe the microwave background defines a preferred reference frame

Relativity of simultaneity does not forbid the actual distribution of stress-energy in the universe from having a particular rest frame.

hence simultaneity is actually absolute.

This is verging on personal speculation and is off limits here. Particularly since it's off topic for this thread anyway.

 

[gentzen]

It's a necessary implication of relativity.

But what does it actually mean? The Thing-in-itself is unknowable. Only representation and observation are knowable. (I took those two words from the linked wiki-page, for concreteness. No need to nitpick.)

This is verging on personal speculation and is off limits here. Particularly since it's off topic for this thread anyway.

It is just an illustration, why I don't see a huge difference between the situation in SR, and my proposed analog for QM.

But if you mean that my analog for QM is personal speculation, then I am fine with it. (As I illustrated with my SEM example, I do believe that this analog contains an important grain of truth.)

I also don't agree that my request for QM analogs (and my specific example of one) are off-topic here. Those analogies between SR and QM are important for RUTA's arguments.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

Reopening thread to reply.

But what does it actually mean?

It means what relativity says it means. We're discussing physics here, not philosophy. Relativity of simultaneity is a perfectly well-defined concept in relativity physics. You're going off into the weeds here.

It is just an illustration

No, it's not, it's denying relativity. Which is not only personal speculation and off topic, but is going against your own intentions relative to the actual topic of this thread:

I also don't agree that my request for QM analogs (and my specific example of one) are off-topic here.

Your basic question about the extent to which the analogy between QM and relativity holds is a perfectly acceptable one. But it's not acceptable to ask that question and then follow it up by denying the very part of relativity that you're asking for a QM analogy of. Please stick to the actual topic.