Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9606025 · Physical Review Letters

Quantum Jumps as Decoherent Histories

Todd A. Brun

Published Mar 10, 1997• 25 citations
arXivHTMLPDF

Abstract

Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jump'' techniques, which solve the master equation by unraveling its evolution into stochastic trajectories in Hilbert space, correspond closely to a particular set of decoherent histories. This is illustrated by a simple model of a photon counting experiment.

DOI
10.1103/physrevlett.78.1833

Related papers

Continuous measurements, quantum trajectories, and decoherent histories

Todd A. Brun

Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum trajectory'' techniques representing continuous measurement schemes, which solve the master equation by unravelling its evolution into stochastic trajectories in Hilbert space, correspond closely to particular sets of decoherent (or consistent) histories. This is illustrated by a simple model of photon counting. An equivalence is shown for these models between standard quantum jumps and the orthogonal jumps of Di\'osi, which have already been shown to correspond to decoherent histories. This correspondence is compared to simple treatments of trajectories based on repeated or continuous measurements.

arXiv:quant-ph/9710021•Physical Review A•Mar 20, 2000•106 citations

Quantum jump unravelings for non-Markovian open system dynamics: a review

Federico Settimo, Jyrki Piilo

Stochastic unravelings provide a useful way to represent open quantum system dynamics in terms of pure state realizations, and have been widely studied both from a fundamental and from a computational point of view. They were initially formulated for Markovian dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad master equation. However, due to recent technological and experimental development, most physical relevant dynamics present temporal correlations beyond the Markov approximation. Such correlations cause decay rates to turn temporarily negative, thus requiring the generalization of stochastic unravelings from Markovian to non-Markovian scenarios. Indeed, many unraveling techniques have been introduced in this regime, and a comprehensive review of the different jump methods is currently missing. In this work, we provide an overview of widely used quantum jump unraveling techniques for non-Markovian systems and also discuss them in terms of their numerical efficiency, divisibility requirements, Hilbert space extension, and measurement interpretation.

quant-pharXiv:2605.07797•May 11, 2026•0 citations

Jump-time unraveling of Markovian open quantum systems

Clemens Gneiting, A. V. Rozhkov, Franco Nori

We introduce jump-time unraveling as a distinct description of open quantum systems. As our starting point, we consider quantum jump trajectories, which emerge, physically, from continuous quantum measurements, or, formally, from the unraveling of Markovian quantum master equations. If the stochastically evolving quantum trajectories are ensemble-averaged at specific times, the resulting quantum states are solutions to the associated quantum master equation. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts. The resulting jump-time-averaged quantum states are then solutions to a discrete, deterministic evolution equation, with time replaced by the jump count. This jump-time evolution represents a trace-preserving quantum dynamical map if and only if the associated open system does not exhibit dark states. In the presence of dark states, on the other hand, jump-time-averaged states may decay into the dark states and the jump-time evolution may eventually terminate. Jump-time-averaged quantum states and the associated jump-time evolution are operationally accessible in continuous measurement schemes, when quantum jumps are detected and used to trigger the readout measurements. We illustrate the jump-time evolution with the examples of a two-level system undergoing relaxation or dephasing, a damped harmonic oscillator, and a free particle exposed to collisional decoherence.

arXiv:2001.08929•Physical Review A•Dec 23, 2021•19 citations

Stochastic jump processes for non-Markovian quantum dynamics

Heinz‐Peter Breuer, Jyrki Piilo

It is shown that non-Markovian master equations for an open system which are local in time can be unravelled through a piecewise deterministic quantum jump process in its Hilbert space. We derive a stochastic Schrödinger equation that reveals how non-Markovian effects are manifested in statistical correlations between different realizations of the process. Moreover, we demonstrate that possible violations of the positivity of approximate master equations are closely connected to singularities of the stochastic Schrödinger equation, which could lead to important insights into the structural characterization of positive non-Markovian equations of motion.

arXiv:0810.5511•Europhysics Letters (EPL)•Mar 1, 2009•59 citations

Decoherent Histories and Quantum State Diffusion

Lajos Diósi, Nicolas Gisin, J. J. Halliwell +1 more

We demonstrate a close connection between the decoherent histories approach to quantum mechanics and the quantum state diffusion picture, for open quantum systems described by a master equation of Lindblad form. The (physically unique) set of variables that localize in the quantum state diffusion picture also define an approximately decoherent set of histories in the decoherent histories approach. The degree of localization is related to the degree of decoherence, and the probabilities for histories prescribed by each approach are essentially the same.

arXiv:gr-qc/9403047•Physical Review Letters•Jan 9, 1995•109 citations

Non-Markovian master equations with quantum trajectory unravellings

James D. Cresser, Sarah Croke

Non-Markovian master equations are constructed from underlying classical stochastic processes. These equations therefore have quantum trajectory unravellings, including unravellings that have an immediate measurement interpretation, usually only found for Markovian (Lindblad) master equations.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2007•0 citations
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jump'' techniques, which solve the master equation by unraveling its evolution into stochastic trajectories in Hilbert space, correspond closely to a particular set of decoherent histories. This is illustrated by a simple model of a photon counting experiment.
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum trajectory'' techniques representing continuous measurement schemes, which solve the master equation by unravelling its evolution into stochastic trajectories in Hilbert space, correspond closely to particular sets of decoherent (or consistent) histories. This is illustrated by a simple model of photon counting. An equivalence is shown for these models between standard quantum jumps and the orthogonal jumps of Di\'osi, which have already been shown to correspond to decoherent histories. This correspondence is compared to simple treatments of trajectories based on repeated or continuous measurements.
Stochastic unravelings provide a useful way to represent open quantum system dynamics in terms of pure state realizations, and have been widely studied both from a fundamental and from a computational point of view. They were initially formulated for Markovian dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad master equation. However, due to recent technological and experimental development, most physical relevant dynamics present temporal correlations beyond the Markov approximation. Such correlations cause decay rates to turn temporarily negative, thus requiring the generalization of stochastic unravelings from Markovian to non-Markovian scenarios. Indeed, many unraveling techniques have been introduced in this regime, and a comprehensive review of the different jump methods is currently missing. In this work, we provide an overview of widely used quantum jump unraveling techniques for non-Markovian systems and also discuss them in terms of their numerical efficiency, divisibility requirements, Hilbert space extension, and measurement interpretation.
We introduce jump-time unraveling as a distinct description of open quantum systems. As our starting point, we consider quantum jump trajectories, which emerge, physically, from continuous quantum measurements, or, formally, from the unraveling of Markovian quantum master equations. If the stochastically evolving quantum trajectories are ensemble-averaged at specific times, the resulting quantum states are solutions to the associated quantum master equation. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts. The resulting jump-time-averaged quantum states are then solutions to a discrete, deterministic evolution equation, with time replaced by the jump count. This jump-time evolution represents a trace-preserving quantum dynamical map if and only if the associated open system does not exhibit dark states. In the presence of dark states, on the other hand, jump-time-averaged states may decay into the dark states and the jump-time evolution may eventually terminate. Jump-time-averaged quantum states and the associated jump-time evolution are operationally accessible in continuous measurement schemes, when quantum jumps are detected and used to trigger the readout measurements. We illustrate the jump-time evolution with the examples of a two-level system undergoing relaxation or dephasing, a damped harmonic oscillator, and a free particle exposed to collisional decoherence.
It is shown that non-Markovian master equations for an open system which are local in time can be unravelled through a piecewise deterministic quantum jump process in its Hilbert space. We derive a stochastic Schrödinger equation that reveals how non-Markovian effects are manifested in statistical correlations between different realizations of the process. Moreover, we demonstrate that possible violations of the positivity of approximate master equations are closely connected to singularities of the stochastic Schrödinger equation, which could lead to important insights into the structural characterization of positive non-Markovian equations of motion.
We demonstrate a close connection between the decoherent histories approach to quantum mechanics and the quantum state diffusion picture, for open quantum systems described by a master equation of Lindblad form. The (physically unique) set of variables that localize in the quantum state diffusion picture also define an approximately decoherent set of histories in the decoherent histories approach. The degree of localization is related to the degree of decoherence, and the probabilities for histories prescribed by each approach are essentially the same.