Quantum jump trajectories, hybrid systems, non-Hermitian evolutions, quantum/classical walks

• URL: http://arxiv.org/abs/2605.01411v1
• Date: Sat, 02 May 2026 12:23:45 GMT
• Title: Quantum jump trajectories, hybrid systems, non-Hermitian evolutions, quantum/classical walks
• Abstract summary: We show how to filter the solution of the non-linear master equation (the conditional state)<n>By the notion of exclusive probability densities" we can describe all the probabilities related to the jumps.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show how to recursively construct the solution of the non-linear stochastic master equation (the conditional state). Moreover, by the notion of ``exclusive probability densities" we can describe all the probabilities related to the jumps, in particular, the waiting times of the jumps and their probability distributions. This general formulation and the idea of hybrid system allow to unify and generalize different fields: evolutions under non-Hermitian Hamiltonians, unitary dynamics interspersed by quantum channels at random times, quantum renewal processes, continuous time open quantum walks, Lindblad rate equation, ...

Related papers

• Current fluctuations in a non-additive open quantum system: breakdown of the quantum-jump approach [0.0]
  Open quantum system dynamics is efficiently described by the quantum master equation formalism.<n>We find that an additive unravelling of the non-additive quantum master equation does not generate a completely-positive dynamics in the scenario of perfect jump detection.
  arXiv  Detail & Related papers  (2026-08-14T16:50:35Z)
• Stochastic Quantum Information Geometry and Speed Limits at the Trajectory Level [35.18016233072556]
  We bridge the gap between quantum information geometry and thermodynamics by introducing the Conditional Quantum Fisher Information (CQFI)<n>We show that the CQFI admits a decomposition into incoherent (population) and coherent (basis rotation) contributions, augmented by a transient interference cross-term absent at the ensemble level.
  arXiv  Detail & Related papers  (2026-01-18T16:23:26Z)
• Open quantum-classical systems: A hybrid MASH master equation [0.0]
  We propose a method which combines the quantum-classical mapping approach to surface hopping (MASH) with the dissipative quantum dynamics of the Lindblad master equation.
  arXiv  Detail & Related papers  (2025-11-07T14:42:44Z)
• Probability-based approach to hybrid classical-quantum systems of any size: Generalized Gleason and Kraus theorems [0.0]
  A fully quantum effective description of hybrid classical-quantum systems is straightforward to formulate when the classical subsystem is discrete.<n>We propose a probability-based approach starting with four axioms for hybrid classical-quantum probability measures.<n>Explicit expressions for these transformations are derived when the classical and quantum subsystems are non-interacting.
  arXiv  Detail & Related papers  (2024-08-20T14:13:44Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
  In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free. We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
  arXiv  Detail & Related papers  (2023-07-05T19:26:09Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• How to design quantum-jump trajectories via distinct master equation representations [0.0]
  We show that there exists inherent freedom in how to assign the terms of the underlying master equation to the jump parts of the description. Our results allow us to get fundamental insights into open quantum system dynamics and to enrich their numerical simulations.
  arXiv  Detail & Related papers  (2020-09-23T18:00:18Z)
• Jumptime unraveling of Markovian open quantum systems [68.8204255655161]
  We introduce jumptime unraveling as a distinct description of open quantum systems. quantum jump trajectories emerge, physically, from continuous quantum measurements. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts.
  arXiv  Detail & Related papers  (2020-01-24T09:35:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.