Testing quantum nonlocality by generalized quasiprobability functions

TL;DR

This paper introduces a new Bell inequality using a generalized quasiprobability function, unifying previous inequalities and demonstrating that the Q function-based inequality can detect quantum nonlocality at lower detector efficiencies.

Contribution

It derives a novel Bell inequality based on a generalized quasiprobability function, encompassing known inequalities and optimizing detection efficiency for nonlocality tests.

Findings

The generalized quasiprobability Bell inequality includes Wigner and Q function inequalities as special cases.

Violations are demonstrated for single photon and two-mode squeezed states.

The Q function-based inequality requires the lowest detector efficiency for nonlocality detection.

Abstract

We derive a Bell inequality based on a generalized quasiprobability function which is parameterized by one non-positive real value. Two types of known Bell inequalities formulated in terms of the Wigner and Q functions are included as limiting cases. We investigate violations of our Bell inequalities for single photon entangled states and two-mode squeezed vacuum states when varying the detector efficiency. We show that the Bell inequality for the Q function allows the lowest detection efficiency for violations of local realism.