Optimal interferometry for Bell$-$nonclassicality by a vacuum$-$one$-$photon qubit

TL;DR

This paper demonstrates how to optimally violate Bell inequalities using weak-field homodyne detection on vacuum-one-photon superpositions, with tunable beamsplitters and photon-number resolution, advancing foundations of quantum physics and quantum protocols.

Contribution

It introduces a method for maximal Bell violation with weak-field homodyne detection, including a condition on measurement settings, applicable to various superpositions.

Findings

Optimal measurement settings involve matching beamsplitter reflectivity to local oscillator strength.

The condition for maximal Bell violation applies to both vacuum-one-photon and photon pair superpositions.

The approach paves the way for device-independent quantum protocols using weak-field homodyne detection.

Abstract

Bell nonclassicality of a single photon superposition in two modes, often referred to as `nonlocality of a single photon', is one of the most striking nonclassical phenomena discussed in the context of foundations of quantum physics. Here we show how to robustly violate local realism within the weak-field homodyne measurement scheme for \textit{any} superposition of one photon with vacuum. Our modification of the previously proposed setups involves tunable beamsplitters at the measurement stations, and the local oscillator fields significantly varying between the settings, optimally being {\it on} or {\it off}. As photon number resolving measurements are now feasible, we advocate for the use of the Clauser-Horne Bell inequalities for detection events using precisely defined numbers of photons. We find a condition for optimal measurement settings for the maximal violation of the Clauser-Horne inequality with weak-field homodyne detection, which states that the reflectivity of the local beamsplitter must be equal to the strength of the local oscillator field. We show that this condition holds not only for the vacuum-one-photon qubit input state, but also for the superposition of a photon pair with vacuum, which suggests its generality as a property of weak-field homodyne detection with photon-number resolution. Our findings suggest a possible path to employ such scenarios in device-independent quantum protocols.