Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup

Dariusz Chruscinski, Gen Kimura, Andrzej Kossakowski, Yasuhito Shishido

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


A general property of relaxation rates in open quantum systems is discussed. We find an interesting constraint for relaxation rates that universally holds in fairly large classes of quantum dynamics, e.g., weak coupling regimes, as well as for entropy nondecreasing evolutions. We conjecture that this constraint is universal, i.e., it is valid for all quantum dynamical semigroups. The conjecture is supported by numerical analysis. Moreover, we show that the conjectured constraint is tight by providing a concrete model that saturates the bound. This universality marks an essential step toward the physical characterization of complete positivity as the constraint is directly verifiable in experiments. It provides, therefore, a physical manifestation of complete positivity. Our conjecture also has two important implications: it provides (i) a universal constraint for the spectra of quantum channels and (ii) a necessary condition to decide whether a given channel is consistent with Markovian evolution.

Original languageEnglish
Article number050401
JournalPhysical Review Letters
Issue number5
Publication statusPublished - 2021 Jul 30

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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