Wave–particle complementarity: detecting violation of local realism with photon-number resolving weak-field homodyne measurements

Abstract

Abstract Nowadays photon-number resolving weak-field homodyne measurements allow realization of emblematic gedankenexperiments revealing correlations of optical fields. This covers experiments on (a) excitation of a pair of spatial modes by a single photon, and (b) two spatial modes in a weakly squeezed vacuum state, involving constant local oscillator strengths. Proving Bell nonclassicality of such correlations demands measurements of complementary observables. We show that typical arrangement of weak-field homodyne detection with measurement settings defined by phases of local oscillators of constant strength does not provide enough complementarity for confirming Bell nonclassicality. In the case of experiment (a) we provide an exact local hidden variable model restoring all quantum probabilities, whereas in the case of experiment (b) we show that the claims of its nonclassicality are unfounded. A full complementarity of wave aspects vs particle (number) can be achieved in a measurement situation in which respectively the local oscillators are on or off. This is shown to lead to an operational scenario, in the case of both experiments (a) and (b), which reveals indisputable violations of local realism. Such schemes may find possible applications in device-independent quantum protocols.