Quantum probability from decision theory?

Barnum, Howard; Caves, Carlton M.; Finkelstein, J.; Fuchs, Christopher A.; Schack, Rüdiger

doi:10.1098/rspa.2000.0557

Cited by 94 publications

(77 citation statements)

References 9 publications

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“…In a recent paper Deutsch (1999) has adopted a different approach based on decision theory. The basic argument focuses again on individual states of quantum systems, but -as noted in the critical comment by Barnum et al (2000) -seems to make appeal to some of the aspects of decision theory that do depend on probabilities. In my view, it also leaves the problem of the phase dependence of the coefficients unaddressed.…”

Section: Other Approaches To Probabilitiesmentioning

confidence: 99%

Decoherence, einselection, and the quantum origins of the classical

2003

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Decoherence is caused by the interaction with the environment which 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 "Schrödinger cat" states. 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 wavepacket". 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: They 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 a 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 the reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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Section: Other Approaches To Probabilitiesmentioning

confidence: 99%

Decoherence, einselection, and the quantum origins of the classical

2003

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“…A widely disputed derivation of the Born rule that is solely based on the non-probabilistic axioms of quantum mechanics and on classical decision theory (and that is more physically motivated than Gleason's argument) has been proposed by Deutsch [14]. It was critized by Barnum et al [15] but was subsequently defended by Wallace [16] and put into an operational framework by Saunders [17]; no decisive conclusion seems to have been reached on the success of these derivations thus far.…”

Section: Introductionmentioning

confidence: 99%

On Zurek?s Derivation of the Born Rule

Schlosshauer

Fine

2005

Found Phys

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“…2 If it is tacitly assumed that his work refers instead to some more orthodox collapse theory, then it is easy to see that the proof is suspect; this is the basis of the criticisms levelled at Deutsch by Barnum et al, (2000). Their attack on Deutsch's paper seems to have been influential in the community; however, it is at best questionable whether or not 2 Nonetheless it is assumed: However, in other respects he [the rational agent] will not behave as if he believed that stochastic processes occur.…”

Section: Introductionmentioning

confidence: 99%

Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation

Wallace

2003

Studies in History and Philosophy of Science Part B: Studies in

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An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this context, it essentially succeeds. Some comments are made about the criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack; it is argued that the flaw which they point out in the proof does not apply if the Everett interpretation is assumed.A longer version of this paper, entitled Quantum Probability and Decision Theory, Revisted, is available online (Wallace 2002). The present paper will appear in Studies in the History and Philosophy of Modern Physics; confusingly, when it does it will also bear the title Quantum Probability and Decision Theory, Revisited.Keywords: Interpretation of Quantum Mechanics -Everett interpretation; Probability; Decision Theory IntroductionIn recent work on the Everett (Many-Worlds) interpretation of quantum mechanics, it has increasingly been recognized that any version of the interpretation worth defending will be one in which the basic formalism of quantum mechanics is left unchanged. Properties such as the interpretation of the wave-function as describing a multiverse of branching worlds, or the ascription of probabilities to the branching events, must be emergent from the unitary quantum mechanics rather than added explicitly to the mathematics. Only in this way is it possible to save the main virtue of Everett's approach: having an account of quantum mechanics consistent with the last seventy years of physics, not one in which the (December 26, 2002 ) * Magdalen College, Oxford University, Oxford OX1 4AU, U.K. (e-mail: david.wallace@magdalen.ox.ac.uk). 1 edifice of particle physics must be constructed afresh (Saunders 1997, p. 44). 1Of the two main problems generally raised with Everett-type interpretations, the preferred-basis problem looks eminently solvable without changing the formalism. The main technical tool towards achieving this has of course been decoherence theory, which has provided powerful (albeit perhaps not conclusive) evidence that the quantum state has a de facto preferred basis and that this basis allows us to describe the universe in terms of a branching structure of approximately classical, approximately non-interacting worlds. I have argued elsewhere (Wallace 2001a(Wallace , 2001b) that there are no purely conceptual problems with using decoherence to solve the preferred-basis problem, and that the inexactness of the process should give us no cause to reject it as insufficient. In particular, the branching events in such a theory can be understood, literally, as replacement of one classical world with several -so that in the Schrödinger Cat experiment, for instance, after the splitting there is a part of the quantum state which should be understood as describing a world in which the cat is alive, and another which describes a world in which it is dead. This multiplication comes about not as a consequen...

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Quantum probability from decision theory?

Cited by 94 publications

References 9 publications

Decoherence, einselection, and the quantum origins of the classical

Decoherence, einselection, and the quantum origins of the classical

On Zurek?s Derivation of the Born Rule

Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation

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