Quantum measurement with chaotic apparatus

Everitt, Mark J.; Munro, William J.; Spiller, Timothy P.

doi:10.1016/j.physleta.2010.05.006

Cited by 12 publications

(27 citation statements)

References 38 publications

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“…The macroscopic size of the pointer then allows observing, storing or processing its outcome. The complete correlations established between S and A by the registration, exhibited inD(t f ) = p iri ⊗D i , entail uniqueness of the outcome s i for the tested observableŝ of S in each run 117 . A filtering of the runs of an ideal measurement, which are tagged by the indication A i of the pointer, therefore constitutes a preparation of the system S, performed through the reduction of S + A (as was anticipated in § 1.1.4) [31].…”

Section: Reduction and Preparations Through Measurementmentioning

confidence: 94%

“…It also turns out that we do not need the additional postulate alluded to at of the end of § 11.1.3, owing to realistic interactions which act within the apparatus at the end of the proces, and which need not play a major role in the truncation and registration 117 But of course there are no well-defined results for observables that do not commute withŝ conditioned by our information. Before acknowledging the outcome of the process, we have to regard it as an element of the full set E of runs issued from the initial stateD(0) of Eq (11.1), and we thus assign to S + A the stateD(t f ) of Eq.…”

Section: Reduction and Preparations Through Measurementmentioning

confidence: 96%

“…It should be noted that, as one would expect, in the classical limit the choice of how to unravel seems to have no effect ons the emergence of a classical dynamic (see, for example, [119]). This implies that the results of [117] may well be independent of the unravelling -but this has yet to be demonstrated.…”

Section: Dutch Proverbmentioning

confidence: 99%

“…Everitt, Munro and Spiller discuss a measurement model which, while fully quantum mechanical, makes use of analogy with classical features of the apparatus [117]. 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].…”

Section: Dutch Proverbmentioning

confidence: 99%

“…The authors of Ref. [117] are aware of this arbitrariness and attempt to minimize it. It should be noted that, as one would expect, in the classical limit the choice of how to unravel seems to have no effect ons the emergence of a classical dynamic (see, for example, [119]).…”

Section: Dutch Proverbmentioning

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: Reduction and Preparations Through Measurementmentioning

confidence: 94%

Section: Reduction and Preparations Through Measurementmentioning

confidence: 96%

Section: Dutch Proverbmentioning

confidence: 99%

Section: Dutch Proverbmentioning

confidence: 99%

Section: Dutch Proverbmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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Looking Forward

Ferry

2024

Quantum Information in the Nanoelectronic World

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Unscrambling the Quantum Omelette

Svozil

2014

Int J Theor Phys

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Based on recent theorems about quantum value-indefiniteness it is conjectured that many issues of "Born's quantum mechanics" can be overcome by supposing that only a single pure state exists; and that the quantum evolution permutes this state.Comment: 6 pages, 2 figures, presented at the "LARSIM/QuPa workshop," Paris, June 28-29, 2012, at "Quantum Structures Cagliari 2012," Cagliari, Sardinia, July 23-27, 2012, as well as at "New Directions in the Foundations of Physics 2013," Washington, D.C., May 10-12, 2013; completely rewritte

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Quantum measurement with chaotic apparatus

Cited by 12 publications

References 38 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Looking Forward

Unscrambling the Quantum Omelette

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