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

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.

arXiv comment5 pages, correct a typo

References in corpus (2)

• Constraints on relaxation rates for N-level quantum systems
• Restriction on relaxation times derived from the Lindblad-type master equations for 2-level systems

Cited by in corpus (8)

• On the universal constraints for relaxation rates for quantum dynamical semigroup
• Theory of the inverse Faraday effect in dissipative Rashba electron systems: Floquet engineering perspective
• Number of steady states of quantum evolutions
• Böttcher-Wenzel inequality for weighted Frobenius norms and its application to quantum physics
• One parameter generalization of BW inequality and its application to open quantum dynamics
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Uncertainty relations based on state-dependent norm of commutator
• Constraints for the spectra of generators of quantum dynamical semigroups