What question did this study set out to answer?

The aim is to develop a framework for analyzing convergence and stability in GKSL dynamics of open quantum systems.

March 18, 2026Open Access

Quantitative Convergence and Spectral-Projector Stability for Finite-Dimensional GKSL Semigroups, with Illustrations on Truncated Bosonic Models

Key Points

The aim is to develop a framework for analyzing convergence and stability in GKSL dynamics of open quantum systems.
Introduced computable bounds for convergence to the asymptotic sector.
Examined perturbative stability of the spectral projection.
Distinguished between primitive and non-primitive semigroups.
Identified unique steady states in primitive semigroups.
Explored multidimensional steady-state structures in non-primitive cases.
Illustrated findings using truncated bosonic models related to quantum memory.

Abstract

We develop a quantitative framework for analyzing convergence and spectral-projector stability in finite-dimensional open quantum systems governed by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) dynamics. Our focus is on computable bounds for the approach to the asymptotic sector and on perturbative stability estimates for the associated spectral projection. We distinguish two geometrically different cases: (i) primitive semigroups with a unique steady state, and (ii) non-primitive semigroups with multidimensional steady-state structure relevant to encoded quantum information. We then illustrate the framework on truncated bosonic models motivated by dissipatively stabilized cat-qubit memories. Validation code and numerical results available at https://doi.org/10.17605/OSF.IO/GP3Z9

Quantitative Convergence and Spectral-Projector Stability for Finite-Dimensional GKSL Semigroups, with Illustrations on Truncated Bosonic Models

Key Points

Abstract

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