Suppose Alice and Bob are arrested for killing Eve, and are taken to two different interrogation rooms. The police quiz Alice and separately Bob, asking them a bunch of different questions along the way. If Alice and Bob can get their stories straight they'll be set free, but if Alice is inconsistent with Bob they'll both be sent to the event horizon of the nearest black hole, to be shredded and spaghettified to smithereens.
But the cops know that Alice and Bob are quantum experimentalists and could have pre-shared some entanglement prior to their arrests. So, the coppers suspect that Alice could be engaging in a CHSH-game with Bob.
Is there anything the cops can do to assure themselves that Alice and Bob did not share any entanglement before being arrested? Is there a set of questions that the cops can ask of Alice and Bob such that they can be assured that Alice and Bob are not engaged in CHSH-like trickery?
At least information-theoretically, I don't think so. I think this is precisely what was ruled out by the no-go theorem on quantum bit commitment. Perhaps there is some post-quantum protocol that can classically bind Alice and Bob, but otherwise I think the cops are stuck assuming Alice and Bob have such entanglement.
