A classification of open Gaussian dynamics

TL;DR

This paper presents a new classification scheme for bosonic open Gaussian dynamics, exploring the conditions for complete positivity and their implications for phase space and quantum information flows.

Contribution

It introduces a comprehensive classification of Gaussian dynamics generators and analyzes the effects of complete positivity constraints on these dynamics.

Findings

Non-symplectic operations are necessary for complete positivity.

Complete positivity restricts volume-conserving non-symplectic operations.

Implications for information and energy flow in open quantum systems.

Abstract

We introduce a classification scheme for the generators of bosonic open Gaussian dynamics, providing instructive diagrams description for each type of dynamics. Using this classification, we discuss the consequences of imposing complete positivity on Gaussian dynamics. In particular, we show that non-symplectic operations must be active to allow for complete positivity. In addition, non-symplectic operations can, in fact, conserve the volume of phase space only if the restriction of complete positivity is lifted. We then discuss the implications for the relationship between information and energy flows in open quantum mechanics.