Completely-positive non-signalling non-Markovian dynamics

Fuente: arXiv
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Main Authors: Kryhin, Serhii, Sudhir, Vivishek
Format: Preprint
Published: 2026
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author Kryhin, Serhii
Sudhir, Vivishek
author_facet Kryhin, Serhii
Sudhir, Vivishek
contents We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.
format Preprint
id arxiv_https___arxiv_org_abs_2605_03197
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Completely-positive non-signalling non-Markovian dynamics
Kryhin, Serhii
Sudhir, Vivishek
Quantum Physics
Other Condensed Matter
Mathematical Physics
Atomic Physics
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.
title Completely-positive non-signalling non-Markovian dynamics
topic Quantum Physics
Other Condensed Matter
Mathematical Physics
Atomic Physics
url https://arxiv.org/abs/2605.03197