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International Journal of Quantum Information

RESTRICTIONS ON INFORMATION TRANSFER IN QUANTUM MEASUREMENTS

Sergey Nikolaevich Mayburov

Published Feb 1, 2007• 2 citations
Publisher

Abstract

Information-theoretical restrictions on the information transfer in quantum measurements are studied for practical systems. For the measurement of quantum system S by information system O such restrictions are described by a formalism of inference maps in Hilbert space, the resulting O restricted states ξO calculated from the agreement with Schrödinger S, O dynamics. It is shown that the principal S information losses stipulate the stochasticity of measurement outcomes; consequently ξO describes the random "pointer" outcomes qj observed by O in the individual events.

DOI
10.1142/s0219749907002748

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Information-theoretical restrictions on the information transfer in quantum measurements are studied for practical systems. For the measurement of quantum system S by information system O such restrictions are described by a formalism of inference maps in Hilbert space, the resulting O restricted states ξO calculated from the agreement with Schrödinger S, O dynamics. It is shown that the principal S information losses stipulate the stochasticity of measurement outcomes; consequently ξO describes the random "pointer" outcomes qj observed by O in the individual events.
Information-theoretical restrictions on the information transferred in quantum measurements are regarded for the measurement of object S performed via its interaction with information system O. This information restrictions, induced by Heisenberg commutation relations, are derived in the formalism of inference maps in Hilbert space. O restricted states ξ O are calculated from S,O quantum dynamics and the structure of O observables set (algebra). It’s shown that this principal constraints on the information transfer result in the appearance of stochasticity in the measurement outcomes. Consequently, ξ O describes the random ’pointer ’ outcomes qj, which correspond to the collapse of S pure state. O decoherence by its environment is studied for some S, O systems, it’s shown that it doesn’t change this results principally. 1
Information-theoretical restrictions on the information transfer in quantum measurements are studied. They are derived for the measurement of system S by detector D, registrated and processed by information system O. The formalism of inference maps in Hilbert space is used for it; it permit to calculate O restricted state which contains all finally available information on S parameters. It's shown that the principal information losses, inevitable in this formalism, stipulate the stochasticity of measurement outcomes registrated by O in the individual events.
Information-theoretical restrictions on the information transfer in quantum measurements are studied. They are derived for the measurement of system S by detector D, registrated and processed by information system O. The formalism of inference maps in Hilbert space is used for it; it permit to calculate O restricted state which contains available for O information on S parameters. It's shown that the principal information losses, inevitable in this formalism and induced by Heisenberg commutation relations, stipulate the stochasticity of measurement outcomes, registrated by O in the individual events.
Information‐theoretical restrictions on the information transferred in quantum measurements, are regarded for the measurement of quantum object S performed via its interaction with information system O. This information restrictions, induced by Heisenberg commutation relations, are derived in the formalism of inference maps in Hilbert space. O restricted states ξo are calculated from Shroedinger S, O dynamics and the structure of O observables set (algebra); O decoherence by its environment is also accounted for some S, O systems. It's shown that this principal constraints on the information transfer result in the stochasticity of measurement outcomes. Consequently, ξo describes the random 'pointer' outcomes qj, which correspond to the collapse of S pure state.
Information-Theoretical restrictions on the systems self-descriptions are applied to Quantum Measurements Theory. For the quantum object S measurement by information system O such restrictions are described by the restricted states formalism by Breuer. The analogous restrictions obtained in Algebraic QM from the analysis of Segal algebra U of O observables; O restricted states set is defined as U dual space. From Segal theorem for the associative subalgebra it's shown that such states describe the random pointer outcomes observed by O in the individual events.
The information transfer in quantum measurements between the measured object Ω and measuring system [Formula: see text] is studied. It was found that due to the quantum-mechanical (QM) constraints, the information about the purity of Ω state is not transferred to [Formula: see text] during the measurement of arbitrary Ω observable V. As a result, [Formula: see text] can not discriminate the pure and mixed Ω ensembles with the same [Formula: see text]. It is shown that such information constraints induce the appearance of stochasticity in the measurement of Ω pure ensemble, so that [Formula: see text] would detect the random a "pointer" coordinates qi; their distribution obeys Born rule. The influence of [Formula: see text] decoherence by its environment is studied, it is shown that the account of its effects does not change this result principally.