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This question is related to Physics SE Objective or Subjective, but is not the same. There was roughly a 10:1 imbalance of answers (weighted by reputation points) to the effect that entanglement is subjective - but this question comes at the issue from a different perspective.

If my understanding is correct, the following statements are true:

  1. Entanglement between a pair of particles is a state variable of the two-particle system, more or less like spin, polarization, or energy.
  2. Entanglement can be measured only by measuring many such pairs that are known to be produced in precisely the same way, and observing correlations in the measurement statistics.

    This leads to the present question:

If absolutely nothing can be known a priori or post priori about the process by which photon pairs are produced, is it possible for photons in the pairs to be entangled?

I've tried to imagine an experiment that could test to see if entanglement is indeterminate -- sort of a Bell's test of entanglement per se. It seems that the experiment would require a way to switch between two different situations: one in which it's possible to know whether or not a given pair of photons is entangled, and one in which it's not possible to know. And, the results of the experiment need to be different in the two cases (by analogy with the double-slit experiment in which any possibility of knowing which slit a photon goes through makes the interference pattern disappear). However, I haven't come up with a suitable experiment yet.

If the answer to the question is “yes”, then it seems that entanglement can't can't really be an indeterminate state variable of the two-photon system – that entanglement would at best be a “hidden variable”.

If the answer is “no”, then it seems that entanglement can't be an intrinsic property of a photon pair: that somehow information about the photon pair production event needs to be available (though not necessarily accessed) along with the photon measurement process in order for there to be entanglement.

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    $\begingroup$ How is this unique to entanglement? Given the restrictions you've placed on the observer's knowledge of the system, every aspect of the system and its quantum state becomes similarly unknowable. Swap out the pair for a single photon and the pair's entanglement for the photon's polarization state, and you get an identical structure. Does that mean that the polarization isn't an intrinsic property of the polarization? $\endgroup$ – Emilio Pisanty Aug 31 '18 at 23:59
  • $\begingroup$ I doubt that it is unique to entanglement; I trust that entanglement is simply an aspect of the mixed quantum state of a multiparticle system. It seems different from a property like polarization - a property of a single particle - though, because polarization of a single photon can be measured and you get an answer. I don't know of a measurement that distinguishes between an entangled pair and an unentangled pair. I realize that measurement of polarization is a projection of the actual polarization probability distribution onto a polarization axis. $\endgroup$ – S. McGrew Sep 1 '18 at 4:10
  • $\begingroup$ If there were a way to measure entanglement of a single pair, then it ought to amount to a projection onto an entanglement "axis", yielding an answer that puts values on the probabilities that the pair is entangled or not. But I suspect no such measurement is possible - or at least meaningful. It would be analogous to measuring the wavefunction, which I understand to be impossible for a single measurement and only possible by making many measurements. So polarization isn't a good analogy for entanglement because one is a state and the other is a distribution of states - a wavefunction. $\endgroup$ – S. McGrew Sep 1 '18 at 4:20
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In the quantum regime, theoretically, everything is entangled. That is what led to the density matrix formulation. For specific situations one has to state the boundary values and the intitial values, and in this case the entanglement can be evident with a single measurement.

Take the $π0->γγ$ decay. One gamma is detected by a spot on a screen, the other in a polarimeter. The person who measures the polarity of the photon knows immediately the polarity of the other , that hit the screen, because the $π0$ has spin zero, and spin is a conserved quantum number.

This "entanglement" terminology is a complicated/confusing way of presenting simple quantum mechanical correlations, imo.

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  • $\begingroup$ Actually, π0−>γγ decay seems to be a good example of a case where additional information is needed in order to detect entanglement. Specifically, we need to know the source of the gamma photons, which separately tells us that the gammas' polarizations are entangled. My question would be, if the source is unknowable can the polarizations be entangled? Given @EmelioPisanty 's answer, it seems that an experiment that could turn the "knowability" of the source on and off should turn the detectability of the entanglement- and therefore the entanglement itself - on and off. $\endgroup$ – S. McGrew Sep 1 '18 at 13:55
  • $\begingroup$ As an experimentalist, I consider this navel "gazing" . y=x^2 +z^2 the variables are entangled whether one gives a value or not. The mathematics describing quantum mechanical systems are entangled, in particular conservation laws , like spin, are always there. It is the platonic ideals mode, making the mathematics create reality. All we have are the quantum mechanical models, and they are validated over and over again. A rocket follows a parabola dictated by the mathematical model whether we look at it or not. Conservation laws are there, whether we look at them or not. That is the model $\endgroup$ – anna v Sep 1 '18 at 14:09
  • $\begingroup$ of reality that we have at present. It might change in the future, and the present model be emergent, but at the moment this is the situation. $\endgroup$ – anna v Sep 1 '18 at 14:09
  • $\begingroup$ Are you saying that it's not possible to turn "knowability" of the source on and off? I can imagine a source in which the (indeterminate) polarization of a "gate photon" allows either an entangled pair to pass, or an unentangled pair to pass. But I think at best we could determine that some entanglement is present but could not determine which pairs are entangled. If the gate photon were itself entangled so we could measure its doppelganger, it would be possible to sort out the entangled pairs from the unentangled pairs with high confidence. $\endgroup$ – S. McGrew Sep 1 '18 at 14:29
  • $\begingroup$ But if you think of them as a "pair" you have already assumed entanglement. I am saying that in our model of the universe everything is entangled in principle, as the algebraic equation I wrote. The universe wave function exists. It is the probabilities that are tiny . With conservation laws we have a handle that can work with probability 1, given initial conditions, as with the pi0 $\endgroup$ – anna v Sep 1 '18 at 15:22

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