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arXiv:quant-ph/0402044

Quantum Measurements and Information Restrictions in Algebraic QM

Sergey Nikolaevich Mayburov

Published Feb 5, 2004• 0 citations
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Abstract

It's argued that Information-Theoretical restrictions for the systems selfdescription are important for Quantum Measurement Problem. They are described by O information system restricted states R formalism by Breuer and can be obtained also in Algebraic QM considering Segal Algebra of O observables. From Segal theorem it's shown that R describes the random measurement outcomes in the individual events.

DOI
10.48550/arxiv.quant-ph/0402044

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It's argued that Information-Theoretical restrictions for the systems selfdescription are important for Quantum Measurement Problem. They are described by O information system restricted states R formalism by Breuer and can be obtained also in Algebraic QM considering Segal Algebra of O observables. From Segal theorem it's shown that R describes the random measurement outcomes in the individual events.
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.
Quantum Measurement problem studied in Information Theory approach of systems selfdescription which exploits the information acquisition incompleteness for the arbitrary information system. The studied model of measuring system (MS) consist of measured state S environment E and observer OOO processing input S signal. OOO considered as the quantum object which interaction with S,E obeys to Schrodinger equation (SE). MS incomplete or restricted states for OOO derived by the algebraic QM formalism which exploits Segal and C∗C^*C∗-algebras. From Segal theorem for systems subalgebras it's shown that such restricted states VO=∣Oj><Oj∣V^O=|O_j> < O_j|VO=∣Oj​><Oj​∣ describes the classical random 'pointer' outcomes OjO_jOj​ observed by OOO in the individual events. The 'preferred' basis ∣Oj>|O_j>∣Oj​> defined by OOO state decoherence via OOO - E interactions.
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 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.