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Communications in Theoretical Physics

Wave-Packet Collapse Based on Weak Repeatability or Covariant Condition*

Zhaoqi Wu, Chuanxi Zhu, Jian-Hui 建辉 Wang 王

Published Feb 1, 2016• 4 citations
Publisher

Abstract

Abstract The conflict between the dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys. Rev. A 76 (2007) 052110], and has further been extended to a more general scenario [Phys. Rev. A 87 (2013) 052111]. In this paper, we reconsider Zurek's new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.

DOI
10.1088/0253-6102/65/2/165

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Abstract The conflict between the dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys. Rev. A 76 (2007) 052110], and has further been extended to a more general scenario [Phys. Rev. A 87 (2013) 052111]. In this paper, we reconsider Zurek's new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.
An unknown quantum state of a single system cannot be discovered, as a measured system is reprepared---it jumps into an eigenstate of the measured observable. This impossibility of finding the quantum state and other symptoms usually blamed on wave-packet collapse follow (as was recently demonstrated for pure states of measured systems) from unitarity (which does not, however, allow for a literal collapse) and from the repeatability of measurements: Continuous unitary evolution and repeatability suffice to establish the discreteness that underlies quantum jumps. Here we consider mixed states of a macroscopic, open system (such as an apparatus), and we allow its microscopic state to change when, e.g., measured by an observer, provided that its salient features remain unchanged and that observers regard macroscopic state of the pointer as representing the same record. We conclude that repeatably accessible states of macroscopic systems (such as the states of the apparatus pointer) must correspond to orthogonal subspaces in the Hilbert space. The symmetry breaking we exhibit defies the egalitarian quantum superposition principle and unitary symmetry of the Hilbert space, as it singles out preferred subspaces. We conclude that the resulting discreteness (which underlies quantum jumps) emerges from the continuity of the core quantum postulates plus repeatability also in macroscopic and open---but ultimately quantum---systems such as measuring devices accessed by observers, where (in contrast with pure states of microsystems) repeatability is paramount.
Chapter 2 shows how the discreteness that sets the stage for discontinuous quantum jumps between a restricted set of states is a consequence of the symmetry breaking that resolves the tension between the unitarity of quantum evolutions, and repeatable information transfer (the essence of quantum Darwinism, the subject of Chapters 7 and 8). Chapter 2 shows that, while the quantum superposition principle declares that every superposition is an equally legal quantum state, repeatability restricts states that can be recorded (found out) multiple times to an orthogonal set determined by the unitary dynamics of the process responsible for the repeated information transfer (i.e., for amplification). Such states persist and can imprint the evidence of their continued presence in other systems, e.g., on the subsystems of the environment. They become the elements of objective reality—e.g., outcomes of the measurements we perceive. Moreover, Chapter 2 motivates the need for the derivation of the probabilities of measurements (to be carried out in Chapter 3).