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Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jumps'' techniques, which solve the master equation by unraveling its evolution into stochastic trajectories in…

Quantum Physics · Physics 2009-10-30 Todd A. Brun

We study joint measurability of quantum observables in open systems governed by a master equation of Lindblad form. We briefly review the historical perspective of open systems and conceptual aspects of quantum measurements, focusing…

Quantum Physics · Physics 2023-09-13 Jukka Kiukas , Pekka Lahti , Juha-Pekka Pellonpää

We demonstrate a close connection between the decoherent histories (DH) approach to quantum mechanics and the quantum state diffusion (QSD) picture, for open quantum systems described by a master equation of Lindblad form. The (physically…

General Relativity and Quantum Cosmology · Physics 2009-10-22 L. Diosi , N. Gisin , J. J. Halliwell , I. G. Percival

The restricted-path-integral (RPI) theory of continuous quantum measurements including the evolution of the measured systems and phenomenon of decoherence is reviewed. The measured system is considered as an open quantum system but without…

Quantum Physics · Physics 2007-05-23 Michael B. Mensky

A large class of non-Markovian quantum processes in open systems can be formulated through time-local master equations which are not in Lindblad form. It is shown that such processes can be embedded in a Markovian dynamics which involves a…

Quantum Physics · Physics 2007-05-23 Heinz-Peter Breuer

This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms…

Quantum Physics · Physics 2025-11-05 Shovan Dutta

Decoherence of a quantum system induced by the interaction with its environment (measuring medium) may be presented phenomenologically as a continuous (or repeated) fuzzy quantum measurement. The dynamics of the system subject to continuous…

Quantum Physics · Physics 2007-05-23 Michael B. Mensky

We consider quantum trajectories of composite systems as generated by the stochastic unraveling of the respective Lindblad-master-equation. Their classical limit is taken to correspond to local jumps between orthogonal states. Based on…

Quantum Physics · Physics 2009-10-31 C. M. Granzow , G. Mahler

We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a…

Quantum Physics · Physics 2017-09-26 A. Chia , T. Paterek , L. C. Kwek

Master equations in the Lindblad form describe evolution of open quantum systems that is completely positive and simultaneously has a semigroup property. We analyze a possibility to derive this type of master equations from an intrinsically…

Quantum Physics · Physics 2007-05-23 Mario Ziman , Peter Stelmachovic , Vladimir Buzek

The Lindblad approach to continuous quantum measurements is applied to a system composed of a two-level atom interacting with a stationary quantized electromagnetic field through a dispersive coupling fulfilling quantum nondemolition…

Quantum Physics · Physics 2009-10-31 Roberto Onofrio , Lorenza Viola

The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which…

Statistical Mechanics · Physics 2025-02-20 Markus Kraft , Mariel Kempa , Jiaozi Wang , Robin Steinigeweg

Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding…

Quantum Physics · Physics 2025-07-23 Calum A. Brown , Katarzyna Macieszczak , Robert L. Jack

We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…

Quantum Physics · Physics 2020-02-11 Anita Dąbrowska , Gniewomir Sarbicki , Dariusz Chruściński

This paper discusses the relation between the decoherent histories approach to quantum mechanics that is based on coarse-grained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in…

Quantum Physics · Physics 2021-11-01 Murray Gell-Mann , James B Hartle

Open quantum systems can be described by unraveling Lindblad master equations into ensembles of quantum trajectories. Here we investigate how the complexity of such trajectories is affected by conservation laws and other dynamical…

Quantum Physics · Physics 2026-05-22 Luca Lumia , Emanuele Tirrito , Mario Collura , Fabian H. L. Essler , Rosario Fazio

Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model,…

Quantum Physics · Physics 2009-11-07 Todd A. Brun

We present a Bayesian algorithm to identify generators of open quantum system dynamics, described by a Lindblad master equation, that are compatible with measured experimental data. The algorithm, based on a Markov Chain Monte Carlo…

Quantum Physics · Physics 2025-09-15 Stewart Wallace , Yoann Altmann , Brian D. Gerardot , Erik M. Gauger , Cristian Bonato

Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. Master equations such as the Lindblad equation preserve the trace of this matrix.…

Quantum Physics · Physics 2009-11-10 A. R. P. Rau , Weichang Zhao

The equivalence of thermodynamic ensembles is at the heart of statistical mechanics and central to our understanding of equilibrium states of matter. Recently, it has been shown that there is a formal connection between the dynamics of open…

Quantum Physics · Physics 2015-07-29 Jukka Kiukas , Madalin Guta , Igor Lesanovsky , Juan P. Garrahan
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