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arXiv:quant-ph/0006104

Relational Quantum Measurements, Information and State Collapse

Sergey Nikolaevich Mayburov

Published Jun 22, 2000• 0 citations
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Abstract

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 $O$.

DOI
10.48550/arxiv.quant-ph/0006104

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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.
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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.