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“Special” states in quantum measurement apparatus: Structural requirements for the recovery of standard probabilities

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Abstract

In a recently proposed quantum measurement theory the definiteness of quantum measurements is achieved by means of “special” states. The recovery of the usual quantum probabilities is related to the relative abundance of particular classes of “special” states. In the present article we consider two-state discrimination, and model the apparatus modes that could provide the “special” states. We find that there are structural features which, if generally present in apparatus, will provide universal recovery of standard probabilities. These structural features relate to the distribution of certain Hamiltonian matrix elements or interaction times. In particular, those quantities must be asymptotically (x → ∞) distributed according to the Cauchy law, Ca(x)=a/π(x2+a2).

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Authors and Affiliations

  1. Institute for Theoretical Physics, State University of Utrecht, PO Box 80006, 3508 TA, Utrecht, The Netherlands

    L. S. Schulman

  2. Physics Department, Clarkson University, 13699-5820, Potsdam, New York

    L. S. Schulman

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  1. L. S. Schulman
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Schulman, L.S. “Special” states in quantum measurement apparatus: Structural requirements for the recovery of standard probabilities. Found Phys 21, 931–945 (1991). https://doi.org/10.1007/BF00733216

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  • DOI: https://doi.org/10.1007/BF00733216

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