Weak unitary symmetries of open quantum dynamics: beyond quantum master equations

TL;DR

This paper investigates the conditions under which weak unitary symmetries are preserved in various descriptions of Markovian open quantum systems, including master equations, joint dynamics, and quantum trajectories, revealing symmetry constraints related to measurements.

Contribution

It provides necessary and sufficient conditions for the preservation of weak symmetries across different descriptions of open quantum dynamics, extending understanding beyond standard quantum master equations.

Findings

Joint dynamics always exhibit a separable symmetry related to the master equation.

Symmetry in quantum trajectories depends on specific conditions of the counting measurement.

Characterization of symmetries in terms of generators for different descriptions.

Abstract

We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation, leading to a closed dynamics for a continuous matrix product state. Performing counting measurements on the environment gives rise to stochastic dynamics of quantum trajectories for the system, which when averaged yield back the quantum master equation. In this work, we identify necessary and sufficient conditions under which the dynamics of these different descriptions retain the weak symmetry of the quantum master equation and we characterise the resulting symmetries of the different descriptions in terms of their generators. We find that the joint dynamics always features a separable symmetry directly related to that of the quantum master equation, but for quantum trajectories the corresponding symmetry is present only if the counting measurement satisfies certain conditions.