Completely-positive non-signalling non-Markovian dynamics

• URL: http://arxiv.org/abs/2605.03197v2
• Date: Wed, 06 May 2026 00:41:50 GMT
• Title: Completely-positive non-signalling non-Markovian dynamics
• Abstract summary: We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states.<n>Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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