The Kossakowski Matrix and Strict Positivity of Markovian Quantum Dynamics

Abstract

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.

References in corpus (5)

• A Brief History of the GKLS Equation
• Irreversible quantum evolution with quadratic generator: Review
• Symmetry and block structure of the Liouvillian superoperator in partial secular approximation
• Exponential Stability of Subspaces for Quantum Stochastic Master Equations
• Reachability in Infinite Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad Generators