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arXiv:quant-ph/9911105

Quantum Information, Irreversibility and State Collapse in Some Microscopic Models of Measurement

Sergey Nikolaevich Mayburov

Published Nov 24, 1999• 0 citations
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Abstract

The quantum measurement problem considered for measuring system (MS) model which consist of measured state S (particle), detector D and information processing device O. For spin chains and other O models the state evolution for MS observables measurements studied. It's shown that specific O states structure forbids the measurement of MS interference terms which discriminate pure and mixed S states. It results in the reduction MS Hilbert space to O representation in which MS evolution is irreversible, which in operational formalism corresponds to S state collapse. In radiation decoherence O model Glauber restrictions on QED field observables results in analogous irreversible MS + field evolution. The results interpretation in Quantum Information framework and Rovelli Relational Quantum Mechanics discussed.

DOI
10.48550/arxiv.quant-ph/9911105

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The quantum measurement problem considered for measuring system (MS) model which consist of measured state S (particle), detector D and information processing device O. For spin chains and other O models the state evolution for MS observables measurements studied. It's shown that specific O states structure forbids the measurement of MS interference terms which discriminate pure and mixed S states. It results in the reduction MS Hilbert space to O representation in which MS evolution is irreversible, which in operational formalism corresponds to S state collapse. In radiation decoherence O model Glauber restrictions on QED field observables results in analogous irreversible MS + field evolution. The results interpretation in Quantum Information framework and Rovelli Relational Quantum Mechanics discussed.
The quantum measurement problem considered for measuring system (MS) consist of measured state S (particle), detector D and information processing device (observer) O. It's shown that O states selfreference structure results in principal nonobservability of MS interference terms which discriminate pure and mixed S states. Such observables restriction permit to construct for MS states subjective representation (SR) which describes probabilistic evolution for measurement events observed by OOO and his subjective information about S values. SR is dual and nonequivalent to MS Hilbert space HHH for external observer O′O'O′. Due to it SR evolution is compatible with Schrodinger linear MS evolution observed by O′O'O′. It's argued that SR evolution corresponds to S state collapse for individual events observed by OOO.
Quantum Measurements regarded in Systems Selfdescription framework for measuring system (MS) consist of measured state S environment E and observer OOO processing input S signal. OOO regarded as quantum object which interaction with S,E obeys to Schrodinger equation (SE) and from it and Breuer selfdescription formalism S information for OOO reconstructed. In particular S state collapse obtained if OOO selfdescription state has the dual structure LT=H⨂LVL_T=\cal H \bigotimes L_VLT​=H⨂LV​ where H\cal HH is Hilbert space of MS states ΨMSΨ_{MS}ΨMS​. LV\cal L_VLV​ is the set with elements VO=∣Oj><Oj∣V^O=|O_j> < O_j|VO=∣Oj​><Oj​∣ describing 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. Zurek's Existential Interpretation discussed in selfmeasurement framework.
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
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 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.
The state vector evolution in the interaction of initial measured pure state with collective quantum system or the field with a very large number of degrees of freedom N is analysed in a nonperturbative QED formalism. As the example the measurement of the electron final state scattered on nucleus or neutrino is considered.In the nonperturbative field theory the complete manifold of the system states is nonseparable i.e. is described by tensor product of infinitely many independent Hilbert spaces. The interaction of this system with the measured state can result in the final states which belong to different Hilbert spaces which corresponds to different values of some classical observables,i.e. spontaneous symmetry breaking occurs. Interference terms (IT) between such states in the measurement of any Hermitian observable are infinitely small and due to it the final pure states can't be distinguished from the mixed ones, characteristic for the state collapse. The evolution from initial to final system state is nonunitary and become formally irreversible in the limit of infinite time. The electromagnetic (e-m) bremmstrahlung produced in the electron scattering process contain the unrestricted number of soft photons which radiation flux become classic observable. Analoguous processes which occurs in the second kind phase transitions in ferromagnetic and phonon excitations in cristall lattice are considered briefly.