Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics

Budini, Adrián A.

doi:10.1103/physreva.88.012124

Cited by 21 publications

(19 citation statements)

References 62 publications

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“…In particular (20) is the standard expression considered in a renewal process describing events randomly taking place after a time interval determined by the distribution f (t). As discussed in [22,23] and detailed in [20] Eqs. (18) and (19) provide a trajectory description of the dynamics at the level of the statistical operator in that they express the solution of the master equation as a sum of contributions corresponding to statistical operators determined by the number and the time of jumps, weighted according to the probability densities (20) and (21).…”

Section: Trajectory Description and Physical Examplesmentioning

confidence: 99%

Generalized Master Equations Leading to Completely Positive Dynamics

Vacchini

2016

Phys. Rev. Lett.

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We provide a general construction of quantum generalized master equations with a memory kernel leading to well-defined, that is, completely positive and trace-preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes and puts into evidence the nonuniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows us to phenomenologically construct a large class of non-Markovian evolutions taking as the starting point collections of time-dependent maps and instantaneous transformations describing the microscopic interaction dynamics.

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Section: Trajectory Description and Physical Examplesmentioning

confidence: 99%

Generalized Master Equations Leading to Completely Positive Dynamics

Vacchini

2016

Phys. Rev. Lett.

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“…Starting from the seminal work in Ref. [29], different approaches have been devised along this line [30,31,32,33,34]. One of us recently extended these results investigating a NM generalization of Eq.…”

Section: Review Of Non-markovian Piecewise Quantum Dynamicsmentioning

confidence: 99%

Quantum Non-Markovian Piecewise Dynamics from Collision Models

Lorenzo

Ciccarello

Palma

et al. 2017

Open Syst. Inf. Dyn.

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Abstract. Recently, a large class of quantum non-Markovian piecewise dynamics for an open quantum system obeying closed evolution equations has been introduced [1]. These dynamics have been defined in terms of a waiting-time distribution between quantum jumps, along with quantum maps describing the effect of jumps and the system evolution between them. Here, we present a quantum collision model with memory, whose reduced dynamics in the continuous-time limit reproduces the above class of non-Markovian piecewise dynamics, thus providing an explicit microscopic realization.

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“…Then, one would expect that n t M ( ) is asymptotically bounded with time, and n t D ( ) can grow with time. However the question of how to partition the bath state B into these two parts, M and D, still has no clear answer, albeit there are investigations and proposals of possible decompositions [41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

Polyakov

Rubtsov

2019

New J. Phys.

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A new approach to theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly bounded on wide time intervals: the occupation of the virtual cloud of quanta. By 'virtual' we denote those bath excitations which were emitted by the open system, but eventually will be reabsorbed before any measurement of the bath state. A useful property of the virtual cloud is that the number of its quanta is expected to saturate on long times, since physically this cloud is a (retarded) polarization of the bath around the system. Therefore, the joint state of open system and virtual cloud (we call it dressed state) can be accurately represented in a truncated basis of Fock states, on a wide time scale. At the same time, there can be an arbitrarily large number of the observable quanta (which survive up to measurement), especially if the open system is under driving. However, it turns out that the statistics of the bathmeasurement outcomes is classical (in a suitable measurement basis): one can employ a Monte Carlo sampling of these outcomes. Therefore, it is possible to efficiently simulate the dynamics of the observable quantum field. In this work we consider the bath measurement with respect to the coherent states, which yields the Husimi function as the positive (quasi)probability distribution of the outcomes. The joint evolution of the dressed state and the corresponding outcome is called the dressed quantum trajectory. The Monte Carlo sampling of these trajectories yields a stochastic simulation method with promising convergence properties on wide time scales.

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Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics

Cited by 21 publications

References 62 publications

Generalized Master Equations Leading to Completely Positive Dynamics

Generalized Master Equations Leading to Completely Positive Dynamics

Quantum Non-Markovian Piecewise Dynamics from Collision Models

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

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