Gravitational Entanglement in Optomechanics: Distinguishing Classical and Quantum Models

TL;DR

This paper investigates how to distinguish classical from quantum gravitational effects in optomechanical systems, emphasizing the importance of non-Gaussian states and negativity measures for detecting non-classicality.

Contribution

It provides a comprehensive analysis of classical and quantum models of gravitational entanglement, proposing operational witnesses based on Wigner negativity and Weyl operator negativity.

Findings

Classical models can mimic quantum entanglement signatures in Gaussian regimes.

Detection of non-classicality requires observing Wigner negativity beyond Gaussian states.

Experimental requirements for certifying gravitational entanglement are more demanding than previously thought.

Abstract

Observation of gravitationally induced quantum entanglement is often interpreted as a direct evidence of non-classical gravity. While the form and the degree of non-classicality have been rigorously studied from a foundational perspective, classical models reproducing experimental signatures of such entanglement remain underexplored. Motivated by the experimental simplicity, nearly all existing optomechanical approaches assume Gaussian initial states, and due to the weakness of gravity the quantum Newtonian potential is truncated at the second order. However, this regime admits a classical description in terms of the Wigner-Weyl representation, including features typically associated with quantum entanglement. A clear distinction between classical and quantum predictions emerges only beyond this setting. We comprehensively analyze the possibilities and provide operational witnesses for detection of non-classicality via Wigner negativity, and detection of non-quantumness via negativity of the Weyl operator. Our results demonstrate that the experimental requirements on certifying gravitational entanglement are more stringent than previously anticipated.