Completely-positive non-signalling non-Markovian dynamics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913093367365632 |
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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 |
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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 |