Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription II: Heisenberg picture and apparent optical entanglement

TL;DR

This paper develops a Heisenberg picture formalism for semiclassical gravity, revealing that classical gravity can induce apparent optical entanglement in optomechanical experiments, potentially mimicking genuine quantum gravity effects.

Contribution

It introduces an equivalent Heisenberg picture formalism for Schroedinger-Newton theory and analyzes its implications for optomechanical experiments testing quantum gravity.

Findings

Classical gravity can induce apparent entanglement in outgoing light fields.

The Heisenberg formalism facilitates analysis of covariance matrices and entanglement features.

Apparent entanglement may lead to false positives in quantum gravity experiments.

Abstract

The evolution of quantum states influenced by semiclassical gravity is distinct from that in quantum gravity theory due to the presence of a state-dependent gravitational potential. This state-dependent potential introduces nonlinearity into the state evolution, of which the theory is named Schroedinger-Newton (SN) theory. The formalism for understanding the continuous quantum measurement process on the quantum state in the context of semiclassical gravity theory has been previously discussed using the Schr\"odinger picture in Paper I [1]. In this work, an equivalent formalism using the Heisenberg picture is developed and applied to the analysis of two optomechanical experiment protocols that targeted testing the quantum nature of gravity. This Heisenberg picture formalism of the SN theory has the advantage of helping the investigation of the covariance matrices of the outgoing light fields in these protocols and further the entanglement features. We found that the classical gravity between the quantum trajectories of two mirrors under continuous quantum measurement in the SN theory can induce an apparent entanglement of the outgoing light field (though there is no quantum entanglement of the mirrors), which could serve as a false alarm for those experiments designed for probing the quantum gravity induced entanglement.