Reduced state of the field and classicality of quantum Gaussian evolution

Abstract

The notion of classicality of quantum evolution of light is an object of both conceptual and practical importance. The main goal of this work is to derive the exact conditions for the classicality of quantum Gaussian evolution, i.e., the evolution of Gaussian states of light and their convex combinations, a model which is of great significance in quantum optics and information. According to our findings, quantum Gaussian evolution should be considered classical if the Hamiltonian and Lindblad operators generating it correspond to passive optical transformations. This is illustrated with several explicit examples, ranging from Gaussian thermal operations to entanglement-maximizing dissipative engineering. Our results are obtained using the recently introduced mesoscopic formalism of the reduced state of the field, which was originally devised as as a description of macroscopic quantum fields. Here, to make the framework suitable for our goal, we redevelop it as a tool for probing classicality, which constitutes our second main contribution.