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Cited by 4,295Quantum Mechanics and ApplicationsQuantum Information and CryptographyAdvanced Thermodynamics and Statistical Mechanics

Decoherence, einselection, and the quantum origins of the classical

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Zurek, Wojciech Hubert·2003·Reviews of Modern Physics
DOI 10.1103/revmodphys.75.715
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Abstract

The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ``Schr\"odinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ``collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ``classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ``found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ``fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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  • Even in the chaotic case, for some examples, the evolution of W_red(q,p,t) approximates the evolution of a classical phase-space distribution W_class(q,p,t), where both distributions rapidly delocalise.

    “On the other hand, at least for some examples it can be shown that, even in the chaotic case, the evolution of W red ( q, p, t ) approximates the evolution of a classical phase-space distribution W class ( q, p, t ) (a Liouville flow with a diffusive contribution from the environment), where both distributions rapidly delocalise (Habib et al . 1998; Zurek 2003, pp. 745-47).”

    From De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial? (2008) · cites this paper as Zurek 2003

  • In certain conditions, the reduced Wigner function W_red(q,p,t) is approximately non-negative and its time evolution approximates that of a classical phase-space distribution.

    “In certain conditions, one obtains an approximately non-negative function W red ( q, p, t ) whose time evolution approximates that of a classical phase-space distribution.”

    From De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial? (2008) · cites this paper as Zurek (2003)

  • This result invalidates claims that there is no general bound valid for all possible (unitary and nonunitary) quantum evolutions.

    “This result invalidates claims that there is no general bound valid for all possible (unitary and nonunitary) quantum evolutions [40].”

    From Quantum Speed Limit for Physical Processes (2013) · cites this paper as [40]

  • Schrödinger pinpointed the role of the randomizing influence of thermal motion, today called environmental decoherence, which separates the quantum from the classical world, an insight often traced to Dieter Zeh.

    “In this, Schrödinger was essentially pinpointing the role of the randomizing influence of thermal motion, what we refer to today as ‘environmental decoherence’ [35], which is what separates the quantum from the classical world, an insight that is often traced back to the work of Dieter Zeh [36].”

    From The origins of quantum biology (2018) · cites this paper as [35]

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Authors
Zurek, W. H.
Affiliations
Los Alamos National Laboratory (US)
Corresponding author
Zurek, Wojciech Hubert
ORCID
Zurek, Wojciech Hubert
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
2003-05-22
Volume
75
Issue
3
Pages
715-775
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
DOI
10.1103/revmodphys.75.715
OpenAlex
W2125303188
Cited by
4,295
References
20
Citations by year
2026: 328 · 2025: 326 · 2024: 199 · 2023: 195 · 2022: 183 · 2021: 196 · 2020: 186 · 2019: 228 · 2018: 187 · 2017: 166 · 2016: 206 · 2015: 170 · 2014: 197 · 2013: 201 · 2012: 201
FWCI
66.35
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Reviews of Modern Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
decoherence, einselection, pointer states, emergence of classicality, Schrödinger cat states, quantum measurement, wave function collapse, open quantum systems, Born rule, envariance, information loss, phase space, quantum foundations

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