Quantifying spectral signatures of non-Markovianity beyond the Born-Redfield master equation

A. Keefe; N. Agarwal; A. Kamal

doi:10.22331/q-2025-09-24-1863

Quantifying spectral signatures of non-Markovianity beyond the Born-Redfield master equation

A. Keefe¹, N. Agarwal¹, and A. Kamal^1,2

¹Department of Physics and Applied Physics, University of Massachusetts, Lowell, MA 01854, USA
²Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA

Published:	2025-09-24, volume 9, page 1863
Editor:	Philip Taranto
Eprint:	arXiv:2405.01722v3
Doi:	https://doi.org/10.22331/q-2025-09-24-1863
Citation:	Quantum 9, 1863 (2025).

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Abstract

Memory or time-non-local effects in open quantum dynamics pose theoretical as well as practical challenges in the understanding and control of noisy quantum systems. While there has been a comprehensive and concerted effort towards developing diagnostics for non-Markovian dynamics, all existing measures rely on time-domain measurements which are typically slow and expensive as they require averaging several runs to resolve small transient features on a broad background, and scale unfavorably with system size and complexity. In this work, we propose a spectroscopic measure of non-Markovianity which can detect persistent non-Markovianity in the system steady state. In addition to being experimentally viable, the proposed measure has a direct information theoretic interpretation: a large value indicates the information loss per unit bandwidth of making the Markov approximation. In the same vein, we derive a frequency-domain quantum master equation (FD-QME) that goes beyond the standard Born-Redfield description and retains the full memory of the state of the reduced system. Using the FD-QME and the proposed measure, we are able to reliably diagnose and quantify non-Markovianity in several system-environment settings including those with environmental correlations and retardation effects.

Featured image: A qubit emission spectrum manifesting non-Markovianity as an off-resonant peak which is directly related bath correlation functions. As this feature becomes more distinguishable, the qubit dynamics deviate more from simple Markovian evolution.

► BibTeX data

@article{Keefe2025quantifyingspectral,
  doi = {10.22331/q-2025-09-24-1863},
  url = {https://doi.org/10.22331/q-2025-09-24-1863},
  title = {Quantifying spectral signatures of non-{M}arkovianity beyond the {B}orn-{R}edfield master equation},
  author = {Keefe, A. and Agarwal, N. and Kamal, A.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1863},
  month = sep,
  year = {2025}
}

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