- #1

DrChinese

Science Advisor

Gold Member

- 7,760

- 1,594

Asking your patience in reading an admittedly long thread post covering what I might call The DrChinese Paradox...

In a recent thread, I argue that Entanglement Swapping + Monogamy Of Entanglement demonstrates "quantum nonlocality" (action at a distance) and "quantum causality" (violation of strict Einsteinian causality). This has the effect of serving as a No-Go for certain QM Interpretations. Any interpretation claiming that swapping can be modeled by statistical post-selection of pre-existing ensembles is necessarily ruled out. Swapping must be an action, a physical event, a projection measurement, an operation, an objective state change, or whatever you want to call it.

Here are a series of references for this thread.

Entanglement Swapping

a. High-fidelity entanglement swapping with fully independent sources (2009)

[We will use their labeling of photons as 1, 2, 3, 4... and the abbreviation BSM as referring to the Bell State Measurement operation on [2 & 3] which leads to the entanglement swap so that [1 & 4] become entangled.]

Entanglement Swapping from Spacetime Separated Sources

b. Characterizing the nonlocal correlations of particles that never interacted (2009)

"

c. Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km

[Note that entanglement swapping can occur even between combinations of electrons and photons.]

d. Entanglement Between Photons that have Never Coexisted (2012)

"

Monogamy Of Entanglement (MOE)

e. Description: https://www.quantiki.org/wiki/monogamy-entanglement

f. Proof: https://arxiv.org/pdf/quant-ph/0604168.pdf

[Conclusion: Given any 3 particles, 2 of which are maximally entangled, the 3rd cannot be entangled with either of the other 2.]

Cascade Entanglement Swapping (6 photons in 3 entangled pairs)

g. Multistage Entanglement Swapping (2008)

"

h. What is generally agreed

No one seems to be contesting the actual experimental results. No one is contesting that the predictions of QM are correct. Everyone agrees that the ordering of the component measurements can be done in any order, and the results will have no statistical change. Everyone agrees that the spacetime distance of the component measurements can be inside or outside common light cones, and the results will have no statistical change. And there is no requirement that the final entangled [1 & 4] photon pair be indistinguishable (after all their individual sources are known), they could for example have different wavelengths.

Further: we should all agree that because the ordering is irrelevant, there is no need to consider reference frames of any kind. The experiments can always be done so that choice of frame leads to identical experimental conclusions, always in agreement with standard non-relativistic QM. Also, we all agree that there is some observer somewhere who is able to see the results of all the components measurements objectively after they have been completed. This allows us to consider a hypothetical "post-selection" scenario which is part of some QM interpretations.

We have previously established that the initial quantum state is a Product State of 2 entangled pairs: $$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}.$$

We have also established that the final quantum state is a Product State of 2 entangled pairs: $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

And I say it should be obvious that: ##\hat{\rho}_{12} \otimes \hat{\rho}_{34} ≠ \hat{\rho}_{23} \otimes \hat{\rho}_{14}## and also ##\hat{\rho}_{12} ≠ \hat{\rho}_{14}##

If you agree with this last conclusion, then we have the following difficulties:

a) Photon [1] could at no time have been maximally entangled with photon [2] and also simultaneously maximally entangled with photon [4]. MOE forbids that.

b) Therefore, "something somewhere" occurred which "quantum causes" (for lack of a better descriptive phrase) the state change of photons [1 & 4] from their initial state to their final entangled state. This despite the fact that [1] is distant from [4] at all times, and the BSM can occur distant to both. What action "caused" the Entanglement Swap? It could *only* have been the BSM performed on photons [2 & 3].

c) The BSM can be performed distant to the [1 & 4] Bell test, leading us to only one possible conclusion: experiments violate Einsteinian locality.

d) They also violate Einsteinian causality, as the BSM can objectively occur either before or after the [1 & 4] is subjected to a Bell test. Because the BSM is a necessary requirement of the Entanglement Swap, it can be considered a "quantum cause".

The only "out" for this last conclusion is a complete rejection of the Monogamy Of Entanglement (MOE), since that is what my argument requires. Yet, MOE is a generally accepted tenet of QM, and is not rejected - as far as I know - by any interpretation. The paradox is therefore that the Pre-existing Correlation Interpretations must reject Monogamy Of Entanglement, but don't and can't.

We have seen one of the problems with reconciling the "Pre-existing Correlations" Interpretations with Monogamy Of Entanglement. Consider an experiment such as g. above where there are 3 entangled photon pairs: [1 & 2], [3 & 4] and [5 & 6]. There are now 2 BSMs (let's call them BSM_23 and BSM_45 - on pairs [2 & 3] and [4 & 5 respectively). Ultimately we perform a Bell test on [1 & 6], which should violate a Bell inequality after BSM_23 and BSM_45 successes. The polarization of photon [1] is tested before BSM_23 is performed. BSM_23 is done before BSM_45, and is also done before the [5 & 6] entangled pair is created.

So: [1] is observed - and ceases to exist - before the [5 & 6] entangled pair is even created. And obviously the swap of entanglement (BSM_45) which comes from identifying which [5 & 6] pairs have suitable statistical correlations to [1] has yet to occur. OK, maybe somehow you can convince yourself that some subensemble of [1] photons and [6] photons will violate a Bell inequality once the [6] photons have been Bell tested.

But we don't even know at this point which [5 & 6] photons are going to be swapped into entanglement with [1] (which no longer even exists). In principle, any entangled pair anywhere in the universe could end up as the [5 & 6] pair. If you had thousands of sources of entangled pairs, they must all in fact contain subensembles that are mutually entangled - where entanglement is mere "Pre-existing Correlations". That conclusion is necessary because there is no act that prevents any entangled pair anywhere in the entire history of the universe from being entangled with the [1] photon we just observed. Because the decision of what photon to swap entanglement with can be made anywhere in the universe, as we already know.

In other words: there can only be a limited number of discrete statistical states that any entangled pair can have, because every stream of entangled pairs has the potential to be swapped with any other entangled pair. This incredible discovery has yet to occur. (Or maybe it just did).

Those Interpretations that follow my Action At A Distance template are viable of course, as there are no contradictions. However, this still does not allow one to distinguish between "quantum nonlocal" Interpretations. Nor does it say what mechanism exists that supports the existing experiments as well as quantum theory.

--------------------------------------------

I have presented experimental evidence that supports the various swapping permutations. And I have presented support and a proof for Monogamy Of Entanglement. The DrChinese paradox is that Pre-existing correlations between independently prepared entangled photon pairs is ruled out by Monogamy Of Entanglement. That's a hard No-Go for quantum interpretations that feature Pre-existing Correlations

Cheers,

-DrC

In a recent thread, I argue that Entanglement Swapping + Monogamy Of Entanglement demonstrates "quantum nonlocality" (action at a distance) and "quantum causality" (violation of strict Einsteinian causality). This has the effect of serving as a No-Go for certain QM Interpretations. Any interpretation claiming that swapping can be modeled by statistical post-selection of pre-existing ensembles is necessarily ruled out. Swapping must be an action, a physical event, a projection measurement, an operation, an objective state change, or whatever you want to call it.

Here are a series of references for this thread.

Entanglement Swapping

a. High-fidelity entanglement swapping with fully independent sources (2009)

[We will use their labeling of photons as 1, 2, 3, 4... and the abbreviation BSM as referring to the Bell State Measurement operation on [2 & 3] which leads to the entanglement swap so that [1 & 4] become entangled.]

Entanglement Swapping from Spacetime Separated Sources

b. Characterizing the nonlocal correlations of particles that never interacted (2009)

"

*Intuitively, it seems that such entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests. To make this intuition concrete and to fully grasp the extent of nonlocality in entanglement swapping experiments, it seems appropriate to contrast them with the predictions of local models...*"c. Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km

[Note that entanglement swapping can occur even between combinations of electrons and photons.]

d. Entanglement Between Photons that have Never Coexisted (2012)

"

*In this work we demonstrate how the time at which quantum measurements are taken and their order, has no effect on the outcome of a quantum mechanical experiment, by entangling two photons that exist at separate times. ... This is a manifestation of the non-locality of quantum mechanics not only in space, but also in time.*"Monogamy Of Entanglement (MOE)

e. Description: https://www.quantiki.org/wiki/monogamy-entanglement

f. Proof: https://arxiv.org/pdf/quant-ph/0604168.pdf

[Conclusion: Given any 3 particles, 2 of which are maximally entangled, the 3rd cannot be entangled with either of the other 2.]

Cascade Entanglement Swapping (6 photons in 3 entangled pairs)

g. Multistage Entanglement Swapping (2008)

"

*Principle of multistage entanglement swapping: three EPR sources produce pairs of entangled photons 1-2, 3-4 and 5-6. Photon 2 from the inial state and photon 3 from the first ancillary pair are subjected to a joint BSM, and so are photon 4 from the first ancillary and photon 5 from the second acillary pair. The two BSMs project outgoing photons 1 and 6 onto an entangled state. Thus the entanglement of the initial pair is swapped to an entanglement between photons 1 and 6.*"h. What is generally agreed

No one seems to be contesting the actual experimental results. No one is contesting that the predictions of QM are correct. Everyone agrees that the ordering of the component measurements can be done in any order, and the results will have no statistical change. Everyone agrees that the spacetime distance of the component measurements can be inside or outside common light cones, and the results will have no statistical change. And there is no requirement that the final entangled [1 & 4] photon pair be indistinguishable (after all their individual sources are known), they could for example have different wavelengths.

Further: we should all agree that because the ordering is irrelevant, there is no need to consider reference frames of any kind. The experiments can always be done so that choice of frame leads to identical experimental conclusions, always in agreement with standard non-relativistic QM. Also, we all agree that there is some observer somewhere who is able to see the results of all the components measurements objectively after they have been completed. This allows us to consider a hypothetical "post-selection" scenario which is part of some QM interpretations.

**The post-selection being the BSM.**So the central question here: can a "Post-Selection = Pre-existing Correlations"**(PC)**Interpretation be considered viable? Or should we require all Interpretations to follow my conclusion, what might be called "Post-Selection = Action At A Distance"**(AAAD)**. Distance in this case should be considered distance in spacetime, i.e. outside of an Einsteinian lightcone.**1. Entanglement Swapping State Change**We have previously established that the initial quantum state is a Product State of 2 entangled pairs: $$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}.$$

We have also established that the final quantum state is a Product State of 2 entangled pairs: $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

And I say it should be obvious that: ##\hat{\rho}_{12} \otimes \hat{\rho}_{34} ≠ \hat{\rho}_{23} \otimes \hat{\rho}_{14}## and also ##\hat{\rho}_{12} ≠ \hat{\rho}_{14}##

**2. The State Change in PC Interpretations (Pre-existing Correlations)**If you agree with this last conclusion, then we have the following difficulties:

a) Photon [1] could at no time have been maximally entangled with photon [2] and also simultaneously maximally entangled with photon [4]. MOE forbids that.

b) Therefore, "something somewhere" occurred which "quantum causes" (for lack of a better descriptive phrase) the state change of photons [1 & 4] from their initial state to their final entangled state. This despite the fact that [1] is distant from [4] at all times, and the BSM can occur distant to both. What action "caused" the Entanglement Swap? It could *only* have been the BSM performed on photons [2 & 3].

c) The BSM can be performed distant to the [1 & 4] Bell test, leading us to only one possible conclusion: experiments violate Einsteinian locality.

d) They also violate Einsteinian causality, as the BSM can objectively occur either before or after the [1 & 4] is subjected to a Bell test. Because the BSM is a necessary requirement of the Entanglement Swap, it can be considered a "quantum cause".

**3. The DrChinese Paradox**The only "out" for this last conclusion is a complete rejection of the Monogamy Of Entanglement (MOE), since that is what my argument requires. Yet, MOE is a generally accepted tenet of QM, and is not rejected - as far as I know - by any interpretation. The paradox is therefore that the Pre-existing Correlation Interpretations must reject Monogamy Of Entanglement, but don't and can't.

**4. More Contradiction/Craziness**We have seen one of the problems with reconciling the "Pre-existing Correlations" Interpretations with Monogamy Of Entanglement. Consider an experiment such as g. above where there are 3 entangled photon pairs: [1 & 2], [3 & 4] and [5 & 6]. There are now 2 BSMs (let's call them BSM_23 and BSM_45 - on pairs [2 & 3] and [4 & 5 respectively). Ultimately we perform a Bell test on [1 & 6], which should violate a Bell inequality after BSM_23 and BSM_45 successes. The polarization of photon [1] is tested before BSM_23 is performed. BSM_23 is done before BSM_45, and is also done before the [5 & 6] entangled pair is created.

So: [1] is observed - and ceases to exist - before the [5 & 6] entangled pair is even created. And obviously the swap of entanglement (BSM_45) which comes from identifying which [5 & 6] pairs have suitable statistical correlations to [1] has yet to occur. OK, maybe somehow you can convince yourself that some subensemble of [1] photons and [6] photons will violate a Bell inequality once the [6] photons have been Bell tested.

But we don't even know at this point which [5 & 6] photons are going to be swapped into entanglement with [1] (which no longer even exists). In principle, any entangled pair anywhere in the universe could end up as the [5 & 6] pair. If you had thousands of sources of entangled pairs, they must all in fact contain subensembles that are mutually entangled - where entanglement is mere "Pre-existing Correlations". That conclusion is necessary because there is no act that prevents any entangled pair anywhere in the entire history of the universe from being entangled with the [1] photon we just observed. Because the decision of what photon to swap entanglement with can be made anywhere in the universe, as we already know.

In other words: there can only be a limited number of discrete statistical states that any entangled pair can have, because every stream of entangled pairs has the potential to be swapped with any other entangled pair. This incredible discovery has yet to occur. (Or maybe it just did).

- Stream B contains some pairs that have Pre-existing Correlations with stream A.
- Stream C contains some pairs that have Pre-existing Correlations with stream A, and some with stream B.
- Stream D contains some pairs that have Pre-existing Correlations with stream A, and some with stream B, and some with stream C.
- Stream E contains some pairs that have Pre-existing Correlations with stream A, and some with stream B, and some with stream C, and some with stream D.
- And so on... for all possible entangled particles in the entire universe, without limit. All of which violate MOE.

**5. The Post-Selection = Action At A Distance Interpretations**Those Interpretations that follow my Action At A Distance template are viable of course, as there are no contradictions. However, this still does not allow one to distinguish between "quantum nonlocal" Interpretations. Nor does it say what mechanism exists that supports the existing experiments as well as quantum theory.

--------------------------------------------

I have presented experimental evidence that supports the various swapping permutations. And I have presented support and a proof for Monogamy Of Entanglement. The DrChinese paradox is that Pre-existing correlations between independently prepared entangled photon pairs is ruled out by Monogamy Of Entanglement. That's a hard No-Go for quantum interpretations that feature Pre-existing Correlations

**(PC)**and deny Action At A Distance**(AAAD)**. I have demonstrated objective distant change of state as a result of a BSM. If you don't like the term "action at a distance" then perhaps you might instead use the less controversial term "quantum nonlocality". Same thing.**Does anyone dispute the agreed facts presented above? And if anyone disagrees with my conclusions, can you provide a specific quote from a suitable source that refutes any specific element of my logic? [No self quotes or references to works allowed here, please!]**Cheers,

-DrC

Last edited: