Quantum violation of stochastic noncontextual hidden-variable theories

Abstract

We formulate stochastic noncontextual hidden-variable theories. In such theories the hidden state λ specifies not definite values, but expectation values A⁻(λ), ... of observables A, ... and noncontextuality means that A⁻(λ) is independent of which other commuting observables commuting with A are measured together with A. We show via Bell inequalities that such theories conflict with quantum theory and propose a two-photon experimental test. We also show that for a single particle of spin (2ⁿ−1)/2, quantum violation of classical noncontextuality grows exponentially with n.