Universal Constraints on Relaxation Times for d-level GKLS master equations

TL;DR

This paper establishes universal bounds on relaxation times for d-level GKLS master equations, extending known results from two-level systems, and offers experimental tests for their validity in quantum dynamics.

Contribution

It generalizes the constraints on relaxation times to d-level systems, providing a new universal inequality that can be experimentally verified.

Findings

Relaxation rate is not greater than half the sum of all relaxation rates.

Constraints serve as tests for complete positivity and Markovianity.

Results applicable to any d-level quantum system.

Abstract

In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered a general form of master equations for an open quantum Markovian dynamics. In honor of all the authors, the equation is nowadays called the GKLS master equation. In this paper, we show universal constraints on the relaxation times valid for any d-level GKLS master equations, which is a generalization of the well-known constraints for 2-level systems. Specifically, we show that any relaxation rate, the inverse-relaxation time, is not greater than half of the sum of all relaxation rates. Since the relaxation times are measurable in experiments, our constraints provide a direct experimental test for the validity of the GKLS master equations, and hence for the conditions of the complete positivity and Markovianity.