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DrChinese

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## Main Question or Discussion Point

Here is one I am having trouble following. Can anyone help me through my confusion?

Our setup is a normal Bell test using entangled photons created using spontaneous parametric down conversion (PDC). Such a setup uses 2 BBO crystals oriented a 90 degrees relative to each other. See for example Dehlinger and Mitchell's http://users.icfo.es/Morgan.Mitchell/QOQI2005/DehlingerMitchellAJP2002EntangledPhotonsNonlocalityAndBellInequalitiesInTheUndergraduateLaboratory.pdf [Broken].

1. Say we have Alice and Bob set their polarizers at identical settings, at +45 degrees relative to the vertical. Once the individual results of Alice and Bob are examined, it will be seen (in the ideal case) that they always match (either ++ or --). According to the local realist or local hidden variables (LHV) advocate, this is "easily" explained:

But that explanation does not seem reasonable to me, even in the case above in which Alice and Bob have identical settings. Here is the paradox as I see it. The source of the photon pairs is the 2 crystals. They achieve an EPR entangled state for testing by preparing a superposition of states as follows:

[tex] |\psi_e_p_r\rangle = \frac {1} {\sqrt{2}} (|V\rangle _s|V\rangle _i + |H\rangle _s|H\rangle _i) [/tex]

This is the standard description per QM. We already know this leads to the [tex] cos^2 \theta [/tex] relationship and the results will be 100% correlation.

The local realist presumably would not accept this description as accurate because it is not complete, and violates the basic premise of any LHV theory. He has an alternate explanation, and the Heisenberg Uncertainty Principle (HUP) is not part of it. So now it appears that our experimental results are compatible with the expectations of both QM and LHV (at least when Alice and Bob have matching settings); however, they have different ways of obtaining identical predictions. But let's look deeper, because I think there is a paradox in the LHV side.

2. Suppose I remove one of the BBO crystals, say the one which produces pairs that are horizontally polarized. I have removed an element of uncertainty of the output stream, as we will now know which crystal was the source of the photon pair. Now the results of Alice and Bob no longer match in all cases, and such is predicted by the application of QM: Alice and Bob will now have matched results only 50% of the time. This follows because the resulting photon pairs emerge from the remaining BBO crystal with a vertical orientation. Each photon has a 50-50 chance of passing through the polarizer at Alice and Bob. But since there is no longer a superposition of states, Alice and Bob do not end up with correlated results.

But what about our LHV theory? We should still get matching results for Alice and Bob because we are still measuring the same attribute on both photons and the conservation rule remains in effect! Yet the actual results are now matches only 50% of the time, no better than even odds.

I mean, if the LHV advocate denies there is superposition in case 1 (such denial is essentially a requirement of any LHV, right?), how does the greater knowledge of the state change anything in case 2?

Our setup is a normal Bell test using entangled photons created using spontaneous parametric down conversion (PDC). Such a setup uses 2 BBO crystals oriented a 90 degrees relative to each other. See for example Dehlinger and Mitchell's http://users.icfo.es/Morgan.Mitchell/QOQI2005/DehlingerMitchellAJP2002EntangledPhotonsNonlocalityAndBellInequalitiesInTheUndergraduateLaboratory.pdf [Broken].

1. Say we have Alice and Bob set their polarizers at identical settings, at +45 degrees relative to the vertical. Once the individual results of Alice and Bob are examined, it will be seen (in the ideal case) that they always match (either ++ or --). According to the local realist or local hidden variables (LHV) advocate, this is "easily" explained:

**if you measure the same attribute of two separated particles sharing such a common origin, you will naturally always get the same answer.**There is no continuing entanglement or spooky action at a distance, and conservation rules are sufficient to provide a suitable explanation. I.e. in LHV theories there is no continuing connection between spacelike separated particles that interacted in the past. The results will be 100% correlation.But that explanation does not seem reasonable to me, even in the case above in which Alice and Bob have identical settings. Here is the paradox as I see it. The source of the photon pairs is the 2 crystals. They achieve an EPR entangled state for testing by preparing a superposition of states as follows:

[tex] |\psi_e_p_r\rangle = \frac {1} {\sqrt{2}} (|V\rangle _s|V\rangle _i + |H\rangle _s|H\rangle _i) [/tex]

This is the standard description per QM. We already know this leads to the [tex] cos^2 \theta [/tex] relationship and the results will be 100% correlation.

The local realist presumably would not accept this description as accurate because it is not complete, and violates the basic premise of any LHV theory. He has an alternate explanation, and the Heisenberg Uncertainty Principle (HUP) is not part of it. So now it appears that our experimental results are compatible with the expectations of both QM and LHV (at least when Alice and Bob have matching settings); however, they have different ways of obtaining identical predictions. But let's look deeper, because I think there is a paradox in the LHV side.

2. Suppose I remove one of the BBO crystals, say the one which produces pairs that are horizontally polarized. I have removed an element of uncertainty of the output stream, as we will now know which crystal was the source of the photon pair. Now the results of Alice and Bob no longer match in all cases, and such is predicted by the application of QM: Alice and Bob will now have matched results only 50% of the time. This follows because the resulting photon pairs emerge from the remaining BBO crystal with a vertical orientation. Each photon has a 50-50 chance of passing through the polarizer at Alice and Bob. But since there is no longer a superposition of states, Alice and Bob do not end up with correlated results.

But what about our LHV theory? We should still get matching results for Alice and Bob because we are still measuring the same attribute on both photons and the conservation rule remains in effect! Yet the actual results are now matches only 50% of the time, no better than even odds.

**What happened to our explanation that "measuring the same attribute" gives identical results?**It seems to me that the only way for a LHV to avoid the paradox is to incorporate the HUP - and maybe the projection postulate too - as a fundamental part of the theory so that it can give the same predictions as QM.I mean, if the LHV advocate denies there is superposition in case 1 (such denial is essentially a requirement of any LHV, right?), how does the greater knowledge of the state change anything in case 2?

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