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The Kossakowski Matrix and Strict Positivity of Markovian Quantum Dynamics

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arxiv 2503.23860 v1 pith:6VMH2B3E submitted 2025-03-31 quant-ph

The Kossakowski Matrix and Strict Positivity of Markovian Quantum Dynamics

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keywords positivitykossakowskimatrixquantumstrictdynamicsirreducibilitymarkovian
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We investigate the relationship between strict positivity of the Kossakowski matrix, irreducibility and positivity improvement properties of Markovian Quantum Dynamics. We show that for a Gaussian quantum dynamical semigroup strict positivity of the Kossakowski matrix implies irreducibility and, with an additional technical assumption, that the support of any initial state is the whole space for any positive time.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dissipation in Periodically Driven Quantum Systems: Partial Secularization and Thermodynamic Consistency

    quant-ph 2026-07 conditional novelty 6.0

    Full secular Floquet master equations force zero steady-state drive power and break the first law; coarse-graining the Floquet–Redfield equation restores complete positivity and consistent currents.