Universal constraint for relaxation rates of semigroups of qubit Schwarz maps

Dariusz Chruściński, Gen Kimura, Farrukh Mukhamedov

Research output: Contribution to journalArticlepeer-review


Unital qubit Schwarz maps interpolate between positive and completely positive maps. It is shown that the relaxation rates of the qubit semigroups of unital maps enjoying the Schwarz property satisfy a universal constraint, which provides a modification of the corresponding constraint known for completely positive semigroups. As an illustration, we consider two paradigmatic qubit semigroups: Pauli dynamical maps and phase-covariant dynamics. This result has two interesting implications: it provides a universal constraint for the spectra of qubit Schwarz maps and gives rise to a necessary condition for a Schwarz qubit map to be Markovian.

Original languageEnglish
Article number185302
JournalJournal of Physics A: Mathematical and Theoretical
Issue number18
Publication statusPublished - May 3 2024


  • Completely positive maps
  • Markovian semigroups
  • Schwarz maps

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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