https://doi.org/10.1140/epjb/s10051-025-01055-5
Research - Condensed Matter
Computable measures of non-Markovianity for Gaussian free fermion systems
1
Dipartimento di Fisica e Astronomia “Ettore Majorana”, Università di Catania, Via S. Sofia 64, 95123, Catania, Italy
2
INFN, Sez. Catania, 95123, Catania, Italy
a
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Received:
17
July
2025
Accepted:
16
September
2025
Published online:
30
September
2025
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.
© The Author(s) 2025
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