Loophole-free Bell test for continuous variables via wave and particle correlations

TL;DR

This paper proposes a new method for a loophole-free Bell test using continuous-variable states, leveraging wave and particle correlations, and demonstrates large violations of Bell inequalities that are robust against detector inefficiencies.

Contribution

It introduces two classes of Bell inequalities for continuous variables that are violated by entangled states with negative partial transposition, enabling loophole-free tests.

Findings

Large violation of inequalities insensitive to detector efficiency

Violations occur only for entangled states negative under partial transposition

Method is feasible with accessible continuous-variable states

Abstract

We derive two classes of multi-mode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure of local realism can be manifested by exploiting wave and particle correlations of readily accessible continuous-variable states, with very large violation of inequalities insensitive to detector-efficiency, which makes a strong case for a loophole-free test.