Decoherence and the Appearance of a Classical World in Quantum Theory

Giulini, Domenico; Joos, E.; Kiefer, Claus; Kupsch, Joachim; Stamatescu, Ion-Olimpiu; Zeh, H. D.

doi:10.1007/978-3-662-03263-3

Cited by 899 publications

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“…Not only Bell's inequalities [27,34,36] but also the Greenberger-Horne-Zeilinger (GHZ) logical paradox [37] have been tested experimentally [38]. Moreover, rather than considering cases where quantum interference terms (the infamous "Schrödinger cat problem" [8,13,39]) vanish owing to decoherence processes [40], experimentalists have become able to control these very interferences [41], which are essential to describe the physics of quantum superpositions of macroscopic states and to explore the new possibilities offered by quantum information [22,42]. Examples include left and right going currents in superconducting circuits [15,43,44,45], macroscopic atomic ensembles [41] and entangled mechanical oscillators [46].…”

Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

“…So let us introduce this concept. Decoherence refers to a process, where due to coupling with an external environment, off-diagonal elements of the system density matrix decay in time; see [32,33,40,199,200,201,202] for reviews. The basis where this decay happens is selected by the structure of the system-environment coupling.…”

Section: Decoherence Theorymentioning

confidence: 99%

“…More recently decoherence has attracted attention as a mechanism of quantum-to-classical transition, and was applied to the quantum measurement problem [32,33,40,199,200,201,202]. The standard pattern of such an application relies on an initial impulsive interaction of the von Neumann type which correlates (entangles) the measuring apparatus with the system to be measured.…”

Section: Decoherence Theorymentioning

confidence: 99%

“…It is often said [32,33,40,199,200,201,202] that "von Neumann's reduction is a decoherence effect". (The traditional word "reduction" covers in the literature both concepts of "truncation" and "reduction" as defined in § 1.3.2.)…”

Section: Truncation Versus Decoherence: a General Phenomenonmentioning

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: General Features Of Quantum Measurementsmentioning

confidence: 99%

Section: Decoherence Theorymentioning

confidence: 99%

Section: Decoherence Theorymentioning

confidence: 99%

Section: Truncation Versus Decoherence: a General Phenomenonmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…4. The Zeno Hamiltonian H Z is given by (26) and turns out to be identical to (44), while the evolution (28) explicitly reads…”

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confidence: 99%

Three Different Manifestations of the Quantum Zeno Effect

Facchi

Pascazio

2003

Irreversible Quantum Dynamics

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The Interpretation of Quantum Mechanics: Many Worlds or Many Words?

1998

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As cutting-edge experiments display ever more extreme forms of non-classical behavior, the prevailing view on the interpretation of quantum mechanics appears to be gradually changing. A (highly unscientific) poll taken at the 1997 UMBC quantum mechanics workshop gave the once alldominant Copenhagen interpretation less than half of the votes. The Many Worlds interpretation (MWI) scored second, comfortably ahead of the Consistent Histories and Bohm interpretations. It is argued that since all the above-mentioned approaches to nonrelativistic quantum mechanics give identical cookbook prescriptions for how to calculate things in practice, practical-minded experimentalists, who have traditionally adopted the "shut-up-and-calculate interpretation", typically show little interest in whether cozy classical concepts are in fact real in some untestable metaphysical sense or merely the way we subjectively perceive a mathematically simpler world where the Schrödinger equation describes everything -and that they are therefore becoming less bothered by a profusion of worlds than by a profusion of words. Common objections to the MWI are discussed. It is argued that when environment-induced decoherence is taken into account, the experimental predictions of the MWI are identical to those of the Copenhagen interpretation except for an experiment involving a Byzantine form of "quantum suicide". This makes the choice between them purely a matter of taste, roughly equivalent to whether one believes mathematical language or human language to be more fundamental.

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Decoherence and the Appearance of a Classical World in Quantum Theory

Cited by 899 publications

References 0 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Three Different Manifestations of the Quantum Zeno Effect

The Interpretation of Quantum Mechanics: Many Worlds or Many Words?

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