The quantum-state diffusion model applied to open systems

Gisin, Nicolas; Percival, I C

doi:10.1088/0305-4470/25/21/023

Cited by 732 publications

(661 citation statements)

References 28 publications

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“…The model consists of a two-level system (the measured system), the apparatus, which is a one-dimensional quartic oscillator under external driving, and an environment whose influence on the system + apparatus is described within the Lindblad master-equation approach and its quantum state diffusion unravelling [118]. The main point of this work is that the apparatus can display the chaotic features of a damped forced non-linear oscillator (and is thus not related to Hamiltonian chaos).…”

Section: Dutch Proverbmentioning

confidence: 99%

“…It is a bad plowman that quarrels with his ox Korean proverb A property that allows us to approach physical reality within the statistical interpretation is the repeatability of ideal measurements 118 . Suppose two successive ideal measurements are performed on the same system S, first with an apparatus A, then, independently, with a similar apparatus A .…”

Section: Repeatability Of Ideal Measurementsmentioning

confidence: 99%

“…The explanation of the appearance, within the quantum theory, of properties seemingly 118 It can be shown that the sole property of repeatability implies reduction in the weak sense, that is, reduction of the marginal state of S [52] 119 Put forward what is true, write it such that it is clear, and fight for it till it is finished with you in contradiction with this very theory relies on several ingredients, exhibited by the detailed solution of the CurieWeiss model. (i) The macroscopic size of the apparatus allows the pointer to relax towards one or another among some possible values, within weak statistical or quantum fluctuations; these outcomes remain unchanged for a long time and can be read or processed; the choice of the a priori equivalent alternatives is triggered by the tested system.…”

Section: Repeatability Of Ideal Measurementsmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Dutch Proverbmentioning

confidence: 99%

Section: Repeatability Of Ideal Measurementsmentioning

confidence: 99%

Section: Repeatability Of Ideal Measurementsmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…The frequently used Monte Carlo or "unravelling" method solves N x M equations, where M brings in the stochasticity of the environment and can be very large , e.g. 100 in [9], 4096 in [43]and 10 7 in [41]). …”

Section: Probabilities For a Two-state System Coupled To A Bosonic Rementioning

confidence: 99%

A “square-root” method for the density matrix and its applications to Lindblad operators

Yahalom

Englman

2006

Physica A: Statistical Mechanics and its Applications

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The evolution of open systems, subject to both Hamiltonian and dissipative forces, is studied by writing the nm element of the time (t) dependent density matrix in the formThe so called "square root factors", the γ(t)'s, are non-square matrices and are averaged over A systems (α) of the ensemble. This square-root description is exact. Evolution equations are then postulated for the γ(t) factors, such as to reduce to the Lindblad-type evolution equations for the diagonal terms in the density matrix. For the off-diagonal terms they differ from the Lindblad-equations. The "square root factors" γ(t) are not unique and the equations for the γ(t)'s depend on the specific representation chosen. Two criteria can be suggested for fixing the choice of γ(t)'s one is simplicity of the resulting equations and the other has to do with the reduction of the difference between the γ(t) formalism and the Lindblad-equations. When the method is tested on cases which have been previously treated by other methods, our results agree with them. Examples chosen are (i) molecular systems, such that are either periodically driven 1 near level degeneracies, for which we calculate the decoherence occurring in multiple Landau-Zener transition, or else when undergoing descent around conical intersections in the potential surfaces, (ii) formal dissipative systems with Lindblad-type operators representing either a non-Markovian process or a two-state system coupled to bosons.Attractive features of the present factorization method are complete positivity, the no higher than linear increase of the implementation effort with the number of states involved and the introduction of randomness only at the start of the process.

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“…A method of treating larger systems in the framework of the QME is the stochastic unraveling of QME (also known as quantum jump, quantum trajectory, and Monte Carlo wave function method) [1,2,34,35,36,37,38,39,41,42,40,5,10,11]. In this method, since one treats a wave function instead of a density matrix, one can investigate systems larger than those in the direct methods.…”

Section: Introductionmentioning

confidence: 99%

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Yuge

Sugita

2015

J. Phys. Soc. Jpn.

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We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part R. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to R to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.

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The quantum-state diffusion model applied to open systems

Cited by 732 publications

References 28 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

A “square-root” method for the density matrix and its applications to Lindblad operators

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

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