Local realism cannot impose commutative structure into noncommuting quantum observables

James D. Malley, Arthur I. Fine

Koji Nagata, Tadao Nakamura

Malley and Fine (Phys. Rev. A 2006 73 066102) discussed that all quantum observables would commute simultaneously if we accept a realistic theory of the Bell type (a local realistic theory) for quantum events, provided that all quantum events, including every quantum state and every observable (including every projector), are reproduced by a realistic theory of the Bell type for quantum events. We point out that their claim leads us to a contradiction. We study the relation between a local realistic theory and commutativity of quantum observables in a finite-dimensional space. We show that a realistic theory of the Bell type for quantum events does not impose the commutative algebraic structure into the set of all quantum observables if all quantum events are reproduced by a local realistic theory. We discuss that a violation of Bell locality is derived within a realistic theory of the Kochen?Specker type within quantum events.

Otto C. W. Kong

Alexander Afriat, F. Selleri

Marek Żukowski, Ryszard Horodecki, Michał Horodecki +1 more

Following the ideas of Popescu, the generic structure of any local hidden variable model for experiments involving sequences of measurements is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are explicitly derived. The violation of local realism in the case of ``hidden nonlocality'' is illustrated by an operational example.

B. Rumbos