Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0205024

Quantum Measurement Problem, Decoherence, and Quantum Systems Selfdescription

Sergey Nikolaevich Mayburov

Published May 6, 2002• 0 citations
arXivHTMLPDF

Abstract

Quantum Measurements regarded in Systems Selfdescription framework for measuring system (MS) consist of measured state S environment E and observer $O$ processing input S signal. $O$ regarded as quantum object which interaction with S,E obeys to Schrodinger equation (SE) and from it and Breuer selfdescription formalism S information for $O$ reconstructed. In particular S state collapse obtained if $O$ selfdescription state has the dual structure $L_T=\cal H \bigotimes L_V$ where $\cal H$ is Hilbert space of MS states $Ψ_{MS}$. $\cal L_V$ is the set with elements $V^O=|O_j> < O_j|$ describing random 'pointer' outcomes $O_j$ observed by $O$ in the individual events. The 'preferred' basis $|O_j>$ defined by $O$ state decoherence via $O$ - E interactions. Zurek's Existential Interpretation discussed in selfmeasurement framework.

DOI
10.48550/arxiv.quant-ph/0205024

Related papers

Quantum Measurement Problem and Systems Selfdescription in Operators Algebras Formalism

Sergey Nikolaevich Mayburov

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 $O$ processing input S signal. $O$ considered as the quantum object which interaction with S,E obeys to Schrodinger equation (SE). MS incomplete or restricted states for $O$ derived by the algebraic QM formalism which exploits Segal and $C^*$-algebras. From Segal theorem for systems subalgebras it's shown that such restricted states $V^O=|O_j> < O_j|$ describes the classical random 'pointer' outcomes $O_j$ observed by $O$ in the individual events. The 'preferred' basis $|O_j>$ defined by $O$ state decoherence via $O$ - E interactions.

arXiv:quant-ph/0212099•Dec 17, 2002•0 citations

Relational Quantum Measurements, Information and State Collapse

Sergey Nikolaevich Mayburov

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 $O$ and his subjective information about S values. SR is dual and nonequivalent to MS Hilbert space $H$ for external observer $O'$. Due to it SR evolution is compatible with Schrodinger linear MS evolution observed by $O'$. It's argued that SR evolution corresponds to S state collapse for individual events observed by $O$.

arXiv:quant-ph/0006104•Jun 22, 2000•0 citations

Quantum Measurement Problem and State Dual Representations

Sergey Nikolaevich Mayburov

The information aspects of quantum measurement problem studied in the simple quantum model of information processing and memorizing device — observer O . It’s argued that to describe probablistic events appearencei, i.e., ‘State Collapse’ consistently O complete states manifold must be tensor product of standard Hilbert space and dual to it novel set describing information acquired by O in the individual events.

Kluwer Academic Publishers eBooks•Feb 24, 2006•0 citations

The ‘Decoherence’ Approach to the Measurement Problem in Quantum Mechanics

Andrew Elby

The decoherence approach to the measurement problem invokes dissipative interactions between a measuring apparatus and its environment to explain, within the context of ‘pure’ quantum mechanics (QM), why such devices appear to possess definite pointer readings. By ‘pure’ QM, I mean Schrödinger evolution with no wavefunction collapse. Several classes of interpretations of pure QM can rely on decoherence. One class is the ‘modal’ interpretations of van Fraassen (1979), Dieks (1989), Healey (1989), and others. Another class is the relative-state and many-world interpretations. I will argue that decoherence cannot help these interpretations address the general metaphysical challenges raised against them. But decoherence can help pick out a ‘special’ basis that determines which observables receive definite values. I'll explore to what extent decoherence rescues the modal (biorthogonal) basis-selection rule, and Zurek's (environmental interaction) basis-selection rule, from the basis degeneracy problem and the imperfect measurement problem.

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1994•16 citations

Information Systems Self-description and Quantum Measurement Problem

Sergey Nikolaevich Mayburov

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.

arXiv:quant-ph/0404153•Apr 27, 2004•0 citations

On Collapse of Quantum State on Measurement

Basudev Nag Chowdhury, Sanatan Chattopadhyay

Abstract In the context of the century-long debate on quantum measurement problem, the current work proposes a model that describes the process of collapse of state by quantum interaction, which resolves the controversies of the framework of quantum mechanics and describes the entire domain of quantum-to-classical world including the weak measurement and partial collapse. ‘Measurement’, being the process of physically interacting with a system in order to extracting information from it, is theorized in the current model by synthesizing the quantum interaction between system and measuring apparatus with the information entropy of such process. The model assumes Schrödinger equation to be the only guiding equation for all physical systems including the measuring apparatus, and does not presuppose ‘superposition principle’, rather derives it theoretically from the formulation. The superposed state is shown to be independent of the choice of measurement operator (observable) or basis states (pointers) of the measuring apparatus. Most interestingly, the current model explains the non-observance of ‘superposition principle’ by classical systems as the classical limit of such quantum description of measurement. Along with solving the quantum measurement problem, the work also explains weak measurement and partial collapse, which can be further extended to investigate such several emerging critical phenomena.

•Jul 27, 2021•1 citation
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.
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.
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.
The decoherence approach to the measurement problem invokes dissipative interactions between a measuring apparatus and its environment to explain, within the context of ‘pure’ quantum mechanics (QM), why such devices appear to possess definite pointer readings. By ‘pure’ QM, I mean Schrödinger evolution with no wavefunction collapse. Several classes of interpretations of pure QM can rely on decoherence. One class is the ‘modal’ interpretations of van Fraassen (1979), Dieks (1989), Healey (1989), and others. Another class is the relative-state and many-world interpretations. I will argue that decoherence cannot help these interpretations address the general metaphysical challenges raised against them. But decoherence can help pick out a ‘special’ basis that determines which observables receive definite values. I'll explore to what extent decoherence rescues the modal (biorthogonal) basis-selection rule, and Zurek's (environmental interaction) basis-selection rule, from the basis degeneracy problem and the imperfect measurement problem.
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.
Abstract In the context of the century-long debate on quantum measurement problem, the current work proposes a model that describes the process of collapse of state by quantum interaction, which resolves the controversies of the framework of quantum mechanics and describes the entire domain of quantum-to-classical world including the weak measurement and partial collapse. ‘Measurement’, being the process of physically interacting with a system in order to extracting information from it, is theorized in the current model by synthesizing the quantum interaction between system and measuring apparatus with the information entropy of such process. The model assumes Schrödinger equation to be the only guiding equation for all physical systems including the measuring apparatus, and does not presuppose ‘superposition principle’, rather derives it theoretically from the formulation. The superposed state is shown to be independent of the choice of measurement operator (observable) or basis states (pointers) of the measuring apparatus. Most interestingly, the current model explains the non-observance of ‘superposition principle’ by classical systems as the classical limit of such quantum description of measurement. Along with solving the quantum measurement problem, the work also explains weak measurement and partial collapse, which can be further extended to investigate such several emerging critical phenomena.