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International Journal of Quantum Information

INFORMATION TRANSFER IN INDIVIDUAL QUANTUM MEASUREMENTS

Sergey Nikolaevich Mayburov

Published Jan 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0219749911007228

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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.
Irreversibility in quantum measurements is considered from the point of quantum information theory. For that purpose the information transfer between the measured object S and measuring system O is analyzed. It's found that due to the principal constraints of quantum-mechanical origin, the information about the purity of S state isn't transferred to O during the measurement of arbitraryS observable V. Consequently O can't discriminate the pure and mixed S ensembles with the same . As the result, the random outcomes should be detected by O in V measurement for S pure ensemble of V eigenstate superposition. It's shown that the outcome probabilties obey to Born rule. The influence of O decoherence by its environment is studied, however the account of its effects doesn't change these results principally.
Quantum-mechanical constraints on information transfer in measuring systems and their influence on measurement results studied. As the example, measurement of binary observable SzS_zSz​ of object S\cal SS by measuring apparatus A\cal AA considered. It's shown that during the measurement these constraints obstacle the acquisition of information by A\cal AA, characterizing purity of S\cal SS ensemble. Due to it, A\cal AA can't discriminate pure and mixed S\cal SS ensembles with the same SzS_zSz​ expectation value. In algebraic measurement ansatz by Emch such information loss results in stochastic SzS_zSz​ measurement outcomes for pure S\cal SS ensemble, their probabilities obey to Born postulate, i.e. it corresponds to quantum state collapse. Account of A\cal AA state decoherence doesn't change obtained results principally.
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 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 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.
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.