A theory of quantum (statistical) measurement
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Publication:6400170
DOI10.1007/S10955-023-03071-0arXiv2205.12906MaRDI QIDQ6400170
Publication date: 25 May 2022
Abstract: We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp's theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and apply it to a model of the Stern-Gerlach experiment. The number N of degrees of freedom of the measuring apparatus is such that , justifying the adjective "statistical", but, in addition, and in contrast to Hepp's approach, we make a three-fold assumption: the measurement is not instantaneous, it lasts a finite amount of time and is, up to arbitrary accuracy, performed in a finite region of space, in agreement with the additional axioms proposed by Basdevant and Dalibard. It is then shown how von Neumann's "collapse postulate" may be avoided by a mathematically precise formulation of an argument of Gottfried, and, at the same time, Heisenbeg's "destruction of knowledge" paradox is eliminated. The fact that no irreversibility is attached to the process of measurement is shown to follow from the author's theory of irreversibility, formulated in terms of the mean entropy, due to the latter's property of affinity.
Operator spaces and completely bounded maps (46L07) Quantum measurement theory, state operations, state preparations (81P15) Measures of information, entropy (94A17) Irreversible thermodynamics, including Onsager-Machlup theory (82B35) Open systems, reduced dynamics, master equations, decoherence (81S22) Quantum state tomography, quantum state discrimination (81P18)
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