Symmetries in open quantum dynamics

TL;DR

This paper explores various symmetries in open quantum dynamics, highlighting how they can reveal properties of subsystems and sometimes imply characteristics of the entire system, beyond traditional constants of motion.

Contribution

It introduces and analyzes new types of symmetries in open quantum systems, especially those depending on correlations and the state of the environment, expanding understanding beyond closed system symmetries.

Findings

Open system symmetries can reveal subsystem properties.

Some symmetries imply properties of the entire system.

Many symmetries depend on correlations with the environment.

Abstract

Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the Hamiltonian has a lower bound, says that the unitary symmetry operator commutes with the Hamiltonian operator. There are many more symmetries that are only for the open dynamics of a subsystem. Examples show how these symmetries alone can reveal properties of the dynamics and reduce what needs to be done to work out the dynamics. A symmetry of the open dynamics of a subsystem can even imply properties of the dynamics for the entire system that are not implied by the symmetries of the dynamics of the entire system. The symmetries are generally not related to constants of the motion for the open dynamics of the subsystem. There are many symmetries that cannot be seen in the Schrodinger picture as symmetries of dynamical maps of density matrices for the subsystem. There are symmetries of the open dynamics of a subsystem that depend only on the dynamics. In the simplest examples, these are also symmetries of the dynamics of the entire system. There are many more symmetries, of a new kind, that also depend on correlations, or absence of correlations, between the subsystem and the rest of the entire system, or on the state of the rest of the entire system.