Computable measures of non-Markovianity for Gaussian free fermion systems

Giuliano Chiriacò ()
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Giuliano Chiriacò: Università di Catania

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 9, 1-10

Abstract: Abstract We investigate measures of non-Markovianity in open quantum systems governed by Gaussian free fermionic dynamics. Standard indicators of non-Markovian behavior, such as the BLP and LFS measures, are revisited in this context. We show that for Gaussian states, trace-based distances—specifically the Hilbert–Schmidt norm—and second-order Rényi mutual information can be efficiently expressed in terms of two-point correlation functions, enabling practical computation even in systems where the full-density matrix is intractable. Crucially, this framework remains valid even when the density matrix of the system is an average over stochastic Gaussian trajectories, yielding a non-Gaussian state. We present efficient numerical protocols based on this structure and demonstrate their feasibility through a small-scale simulation. Our approach opens a scalable path to quantifying non-Markovianity in interacting or measured fermionic systems, with applications in quantum information and non-equilibrium quantum dynamics. Graphic Abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-01055-5

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