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 TMF, 2011, Volume 168, Number 1, Pages 65–79 (Mi tmf6664)

Representation and interpretation of quantum mixtures in the ESR model

C. Garola, S. Sozzo

Dipartimento di Fisica dell'Università del Salento, INFN-Sezione di Lecce, Lecce

Abstract: The interpretation of mixtures is problematic in quantum mechanics (QM) because physical properties are nonobjective in this theory. An extended semantic realism model was recently developed, restoring objectivity by reinterpreting quantum probabilities as conditional on detection and embodying the QM mathematical formalism in a broader noncontextual (hence local) framework. In this model, each generalized observable is represented by a family of positive operator-valued measures parameterized by the pure states of the considered physical system $\Omega$. We here propose a new proof that each proper mixture is represented by a family of density operators parameterized by the macroscopic properties characterizing $\Omega$. We then show that this representation implies some predictions differing from the QM predictions and avoids the problems following from the standard QM representation of proper mixtures. We also recall that the state transformations induced by idealized nondestructive measurements can be obtained using a nontrivial generalization of the Lüders postulate.

Keywords: quantum mechanics, quantum mixture, quantum probability, Lüders postulate

DOI: https://doi.org/10.4213/tmf6664

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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 912–923

Bibliographic databases:

Citation: C. Garola, S. Sozzo, “Representation and interpretation of quantum mixtures in the ESR model”, TMF, 168:1 (2011), 65–79; Theoret. and Math. Phys., 168:1 (2011), 912–923

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf6664
• https://doi.org/10.4213/tmf6664
• http://mi.mathnet.ru/eng/tmf/v168/i1/p65

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Garola C., Sozzo S., “Extended representations of observables and states for a noncontextual reinterpretation of QM”, J. Phys. A, 45:7 (2012), 075303, 13 pp.
2. Sozzo S., “The Quantum Harmonic Oscillator in the Esr Model”, Found. Phys., 43:6 (2013), 792–804
3. C. Garola, M. Persano, J. Pykacz, S. Sozzo, “Finite local models for the GHZ experiment”, Int. J. Theor. Phys., 53:2 (2014), 622–644
4. Garola C., Persano M., “Embedding Quantum Mechanics Into a Broader Noncontextual Theory”, Found. Sci., 19:3 (2014), 217–239
5. Garola C., “a Survey of the Esr Model For An Objective Reinterpretation of Quantum Mechanics”, Int. J. Theor. Phys., 54:12 (2015), 4410–4422
6. Garola C., Sozzo S., Wu J., “Outline of a Generalization and a Reinterpretation of Quantum Mechanics Recovering Objectivity”, Int. J. Theor. Phys., 55:5 (2016), 2500–2528
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