Violating the Leggett-Garg inequalities with classical light

TL;DR

This paper demonstrates that classical states of light, including coherent and thermal states, can violate Leggett-Garg inequalities, challenging the notion that such violations are exclusive to quantum systems.

Contribution

It shows that classical light states can violate Leggett-Garg inequalities using negative measurements, expanding the understanding of non-classicality beyond quantum systems.

Findings

Classical states of light can violate Leggett-Garg inequalities.

Violation persists even without initial phase reference.

Thermal states of light can also demonstrate violations.

Abstract

In an endeavour to better define the distinction between classical macroscopic and quantum microscopic regimes, the Leggett-Garg inequalities were established as a test of macroscopic-realistic theories, which are commonly thought to be a suitable class of descriptions for classical dynamics. The relationship between their violation and non-classicality is however not obvious. We show that classical states of light, which in the quantum optical sense are any convex sums of coherent states, may not satisfy the Leggett-Garg inequalities. After introducing a simple Mach-Zehnder setup and showing how to obtain a violation with a single photon using negative measurements, we focus on classical states of light, in particular those of low average photon number. We demonstrate how one can still perform negative measurements with an appropriate assignment of variables, and show that the inequalities are violable with coherent states. Finally, we abandon initial phase reference and demonstrate that the violation is still possible, in particular with thermal states of light, and we investigate the effect of intermediate dephasing.