Interpreting photon correlations from independent sources

[javisot20]

The entanglement you describe is strictly prohibited in orthodox quantum theory. There can be no entangled (1&2&3), for example. See the seminal work here or a short proof here. The subject is Monogamy of Entanglement.

Nothing like what describe occurs in entanglement swapping.

What I have said is that 2&3, which is 1 system, is entangled with 1, or 4 (or 1&4). One system is entangled with another, not three or four entangled systems.

(I say this playing devil's advocate, trying to understand the point of view of someone who defends the locallity to understand the experimental results, influenced by this thread and the consistent history and locality thread, mainly)

 

[PeterDonis]

What I have said is that 2&3, which is 1 system, is entangled with 1, or 4 (or 1&4).

No, that's not correct.

Initially (before the BSM), photons 1&2 form an entangled system, and photons 3&4 form an entangled system. Those two systems are separable; they are not entangled at all.

If no swap occurs, the entanglements remain as stated above.

If a swap does occur, then after the swap, photons 2&3 form an entangled system, and photons 1&4 form an entangled system, and those two systems are separable; they are not entangled at all.

There is never a time when photons 2&3, as a system (meaning they are entangled with each other), are entangled with 1, or 4, or both.

 

[Morbert]

@DrChinese I believe our primary disagreement is over 1., so I will address this for now and we can proceed to your other points once it is resolved. I suspect the resolution of our primary disagreement would impact how other points are addressed anyway.

Of course I agree completely with Ma et al. As I answered this question in the other thread, so I answer here.

1. Your question regarding the 2 & 3 photons (b and c detectors in the Ma paper): Is HH (swap) = HH' (no swap) and VV (swap) = VV' (no swap) ? In other words, are they measuring the same/equivalent characteristics (apples to apples)? Do the results stay the same after the beam splitter regardless of whether a swap is performed? Can we be sure a swapped HV or VH doesn't get wrongly reported as an HH or VV as a result of an hypothetical overlap effect in the beam splitter?

Well of course the answer is YES, we can be sure. It has to be, this is physically dependent on the polarization characteristics of a beam splitter - which are essentially none for our purposes. No amount of interference or interaction between 2 photons overlapping in the beam splitter is going to change H to V (or vice versa). There is no evidence otherwise, and there is no theory to support that speculative idea. It is easily testable, although I have never seen such an experiment. (Of course, there are many experiments one might perform to confirm the predictions of QM that have never been performed.)

HV or VH are less helpful as they must always be discarded.

Victor's detector coincidences with one horizontal and one vertical photon in spatial modes b’’ and c’’ indicate the states |𝐻𝑉〉 23 and |𝑉𝐻〉 23, which are always discarded because they are separable states independent of Victor’s choice and measurement.

So to more accurately reflect the subsets, and if I am reading the paper correctly, they are {HH, VV, discarded} for the SSM and {Φ+, Φ-, discarded} for the BSM.

If your answer is still yes for the HH and VV cases, then why doesn't this run afoul of complemenetarity?

These two measurements are mutually exclusive (complementary in the Bohrian sense) in the same way as measuring particle or wave properties in an interference experiment.

E.g. say I perform a BSM and the detectors fire indicating (b'', H) and (c'', H). I can therefore infer the BSM result Φ- as described by Ma. You seem to be implying I can also infer the SSM result HH, but how can this be? These are results of complementary measurements. How can I infer HH from a result

Φ− = (HH − VV)/√2

 

[javisot20]

There is never a time when photons 2&3, as a system (meaning they are entangled with each other), are entangled with 1, or 4, or both.

This is the point at which many conclude, "nonlocality is proven," right?

 

[DrChinese]

This is the point at which many conclude, "nonlocality is proven," right?

“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” - Arthur Conan Doyle

Just saying… we need to identify assumptions and question them. Mother Nature seems to be a trickster.

 

[javisot20]

“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.” - Arthur Conan Doyle

Just saying… we need to identify assumptions and question them. Mother Nature seems to be a trickster.

Therefore, a person who wants to deny non-locality must deny the above, and affirm that 1 and 4 did interact locally with each other, using 2 and 3 as intermediaries, and we already know that 2 and 3 are intermediaries between 1 and 4. At this point others will say that the locality is proven.

Whether we affirm locality or non-locality, everyone agrees that the swap or non-swap of 2&3 will affect 1&4.

 

[DrChinese]

Φ@DrChinese I believe our primary disagreement is over 1., so I will address this for now and we can proceed to your other points once it is resolved. I suspect the resolution of our primary disagreement would impact how other points are addressed anyway.

1. HV or VH are less helpful as they must always be discarded. So to more accurately reflect the subsets, and if I am reading the paper correctly, they are {HH, VV, discarded} for the SSM and {Φ+, Φ-, discarded} for the BSM.

2. If your answer is still yes for the HH and VV cases, then why doesn't this run afoul of complemenetarity?E.g. say I perform a BSM and the detectors fire indicating (b'', H) and (c'', H). I can therefore infer the BSM result Φ- as described by Ma. You seem to be implying I can also infer the SSM result HH, but how can this be? These are results of complementary measurements. How can I infer HH from a result

Φ− = (HH − VV)/√2

1. Again, you have this backwards. In the experiment, all 4 fold coincidences with HH or VV for the b” and c” polarizers are reported. Your hypothesis boils down to saying some of the HV or VH get misreported as HH or VV. If that happened, it would be reported as you say - and would bias the results, possibly overstating the correlation.

Keep in mind that what they are reporting is HH/VV (the signature) but that is an SSM if no swap and Φ− if BSM. We agree on this point.

2. Again, the HH/VV signature is identical for the reported BSM or SSM. In case this is not clear: there is no way to know if there was a swap or not by looking to the b” and c” results. Either way, there will be one click at a b” detector and one click at a c” - and they will both be H or both V. To know if a swap occurred, you also need to know what the setting of the beam splitter is.

So I think we agree on this. You therefore also know that if the setting had been the complementary option, you would get the same outcomes for b” and c”. No difference, which answers your question/criticism. The b”/c” results are the same, but the Alice/Bob results appear to change.

 

[DrChinese]

Therefore, a person who wants to deny non-locality must deny the above, and affirm that 1 and 4 did interact locally with each other, using 2 and 3 as intermediaries, and we already know that 2 and 3 are intermediaries between 1 and 4. At this point others will say that the locality is proven.

Whether we affirm locality or non-locality, everyone agrees that the swap or non-swap of 2&3 will affect 1&4.

Of course, 1 and 4 are never in a common light cone. And 2 and 3 can be observed long after 1 and 4 are measured. I would claim all measurements are causally disconnected from each other.

 

[PeterDonis]

1 and 4 did interact locally with each other, using 2 and 3 as intermediaries

I don't know of any feasible meaning of the word "locally" that would support such a claim. Note that, as @DrChinese has pointed out, photons 2&3 can interact long after photons 1&4 are measured. And the photon 1&4 measurements could, in principle, be many light-years apart, and many light-years separated from the photon 2&3 interaction.

 

[Morbert]

1. Again, you have this backwards. In the experiment, all 4 fold coincidences with HH or VV for the b” and c” polarizers are reported. Your hypothesis boils down to saying some of the HV or VH get misreported as HH or VV. If that happened, it would be reported as you say - and would bias the results, possibly overstating the correlation.

Keep in mind that what they are reporting is HH/VV (the signature) but that is an SSM if no swap and Φ− if BSM. We agree on this point.

2. Again, the HH/VV signature is identical for the reported BSM or SSM. In case this is not clear: there is no way to know if there was a swap or not by looking to the b” and c” results. Either way, there will be one click at a b” detector and one click at a c” - and they will both be H or both V. To know if a swap occurred, you also need to know what the setting of the beam splitter is.

So I think we agree on this. You therefore also know that if the setting had been the complementary option, you would get the same outcomes for b” and c”. No difference, which answers your question/criticism. The b”/c” results are the same, but the Alice/Bob results appear to change.

This is the time-evolution relevant to the BSM result Φ−, taken from Ma et al

So you can see that the issue is not HV or VH getting misreported as HH or VV. It's that "VV" could be "misreported" as "HH" or vice versa. To put it more correctly, when a BSM is carried out, a signature like (H b", H c'') only lets you infer (HH - VV)/√2. It does not let you infer HH.

 

[DrChinese]

… To put it more correctly, when a BSM is carried out, a signature like (H b", H c'') only lets you infer (HH - VV)/√2. It does not let you infer HH.

I don’t follow your thinking, so maybe you can help me.

For the BSM cases:

The HH and VV signatures (photons 2 and 3) are reported together. So this point doesn’t affect the experimental results and conclusion in any way. Hopefully this is not in question.

Now if you ask: what does it tell us about the associated 1 and 4 photons: you would be correct to say that those results need not match the 2 and 3 signatures, when measured on the same H/V basis. Of course, they will be perfectly correlated on any same basis. Hopefully I agree with you here as well.

So… what are you trying to get across?