All quantum observables in a hidden-variables model must commute simultaneously

Details All quantum observables in a hidden-variables model must commute simultaneously All quantum observables in a hidden-variables model must commute simultaneously

2004-02-18

arxiv.org/abs/quant-ph/0402126v1

Physics

Quantum Physics

This is an expanded version of the paper scheduled to appear in Physical Review A (Feb 2004), and includes a rather long techn

Scientific paper

10.1103/PhysRevA.69.022118

Under a standard set of assumptions for a hidden-variables model for quantum events, we show that all observables must commute simultaneously. And, despite Bell's complaint that a key condition of von Neumann's was quite unrealistic, we show these these conditions are entirely equivalent to those later introduced by Bell, Kochen and Specker. As is it known that these conditions are also equivalent to those under which the Bell-Clauser-Horne inequalities are derived, we see that any experimental violations of the inequalities demonstrate only that quantum observables do not commute.The same conclusion applies to the collection of elegant inequality-free no-go proofs of Greenberger-Horne-Zeilinger, Mermin and Peres. Otherwise expressed, the usual hidden-variable models have assumptions that are collectively too strong to be interesting, and hence need modification or deletion.

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