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Jun 22, 2014 at 22:00 comment added celtschk A third way to prepare the same $\rho$ is to generate a polarization-entangled two-photon state and send one of the photons. If you retain the other photon, you can turn the sent-out photon into either Alice's or Bob's ensemble by measuring the other photon in either the horizontal/vertical or circular polarization basis. Note that the actual measurement statistics of the sent-out photon won't depend on which way (or even whether) you measured the second photon.
Feb 12, 2014 at 9:10 comment added Valter Moretti However, considering the state prepared by, say Bob, even it is not perfectly unpolarized it is described by some density matrix $\rho$ "close" to $I/2$. No matter its specific form, you can always write it as an incoherent superposition of pure states different from those used by Bob, corresponding to a different experimental preparation. Once the state has been constructed you cannot distinguish between the two preparations by measuring any observable on the state. That is my point.
Feb 12, 2014 at 4:27 history answered Steve Byrnes CC BY-SA 3.0