On detecting violation of local realism with photon-number resolving weak-field homodyne measurements

TL;DR

This paper challenges claims that certain weak-field homodyne measurements with photon-number resolution cannot be explained by local hidden variable models, providing an exact LHV model for specific quantum states and measurements.

Contribution

It introduces an exact local hidden variable model for photon-number resolving weak-field homodyne measurements on specific quantum states, disputing previous claims of non-locality.

Findings

An exact LHV model resolves the 'non-locality of a single photon' dispute.

Measurements with local oscillators on or off lack LHV models.

The model applies to excitation of a photon pair and weakly squeezed vacuum states.

Abstract

Non-existence of a local hidden variables (LHV) model for a phenomenon benchmarks its use in device-independent quantum protocols. Nowadays photon-number resolving weak-field homodyne measurements allow realization of emblematic gedanken experiments. Alas, claims that we can have no LHV models for such 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, are unfounded. For (a) an exact LHV model resolves the dispute on the "non-locality of a single photon" in its original formulation. It is measurements with local oscillators on or off that do not have LHV models.