A Feasible Quantum Optical Experiment Capable of Refuting Noncontextuality for Single Photons

Elaborating on a previous work by Simon et al. [Phys. Rev. Lett. 85, 1783 (2000)] we propose a realizable quantum optical single-photon experiment using standard present day technology, capable of discriminating maximally between the predictions of quantum mechanics (QM) and noncontextual hidden variable theories (NCHV). Quantum mechanics predicts a gross violation (up to a factor of 2) of the noncontextual Bell-like inequality associated with the proposed experiment. An actual maximal violation of this inequality would demonstrate (modulo fair sampling) an all-or-nothing type contradiction between QM and NCHV. An essential feature inherent in the world picture presented to us by classical physics is that the measured values of any dynamical variable A ascribed to an individual system are context independent, that is, they do not depend on what other commeasurable variables B, C, . . . are measured along with it. This central tenet is captured by the so-called noncontextual hidden variable (NCHV) theories which assume that the result of a measurement of A depends solely on the choice of A and on the state of the system being measured (the state being fully described by certain (noncontextual) hidden variables). While quantum mechanics (QM) satisfies this noncontextuality condition for the expectation value of the observables, the Bell–Kochen–Specker theorem [1–3] shows that noncontextuality is incompatible with the predictions that QM makes for single individual systems, provided the dimension of the associated Hilbert space is greater than two. Experimentally speaking, however, there have been relatively very few experiments testing the validity of the general assumption of noncontextuality, in contrast to the many experiments performed to test Bell’s theorem [4] against local hidden variables (LHV) [5]. Indeed, to our knowledge, the recent two experiments performed by Michler et al. [6] are the first explicitly implementing a statistical test of NCHV versus ∗Electronic mail: [email protected]