Mermin's One-Measurement Refutation of Local Hidden Variables

[stevendaryl]

I remember an argument, I think due to David Mermin, that refutes local hidden variables in a single measurement (as opposed to Bell's Inequality, which requires gathering statistics of many measurements). I know that's not a lot to go on, but I'm wondering if this rings a bell (no pun intended)? The idea was that there was a single measurement (or maybe a fixed finite number of measurements) such that the prediction of any local hidden variables theory was one thing, and the prediction of quantum mechanics was something else.

 

[jk22]

I think there is one argument due to von Neumann and taken again by Bell : if you measure the sum let say spin_x+spin_z, then a hidden variable would have to associate 1 and -1 for each spin, but the sum has eigenvalue sqrt(2) which is not the sum of the hidden variable result. Was it that ?

 

[stevendaryl]

No, I don't think that was it. As I said, I think it was a more recent argument due to David Mermin.

 

[Demystifier]

I remember an argument, I think due to David Mermin, that refutes local hidden variables in a single measurement (as opposed to Bell's Inequality, which requires gathering statistics of many measurements). I know that's not a lot to go on, but I'm wondering if this rings a bell (no pun intended)? The idea was that there was a single measurement (or maybe a fixed finite number of measurements) such that the prediction of any local hidden variables theory was one thing, and the prediction of quantum mechanics was something else.

You are probably talking about GHZ and Hardy proofs of nonlocality, which were reviewed and simplified by Mermin. The GHZ and Hardy proofs involve equalities rather than inequalities, such that only a few measurements are sufficient to disprove them, in agreement with quantum mechanics.