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arXiv · 2605.03197

Completely-positive non-signalling non-Markovian dynamics

Serhii Kryhin·Vivishek Sudhir
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Abstract

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.

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Serhii Kryhin, Vivishek Sudhir. 2026-05-06. Completely-positive non-signalling non-Markovian dynamics. https://arxiv.org/abs/2605.03197

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