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The Extended Bloch Representation of Entanglement and Measurement in Quantum Mechanics

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Abstract

The quantum formalism can be completed by assuming that density operators also represent genuine states. An ‘extended Bloch representation’ (EBR) then results, in which not only the states but also the measurement-interactions can be described. Consequently, the Born rule can be obtained as an expression that quantifies the lack of knowledge about the measurement-interaction that is each time actualized, during a measurement. Entanglement can also be consistently described in the EBR, as it remains compatible with the principle according to which a composite entity exists only if its components also exist, and therefore are in well-defined states.

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Authors and Affiliations

  1. Center Leo Apostel (Clea), Brussels Free University (VUB), Pleinlaan 2, 1050, Brussel, Belgium

    Diederik Aerts

  2. Laboratorio di Autoricerca di Base, 6914, Lugano, Switzerland

    Massimiliano Sassoli de Bianchi

  3. School of Business and Institute IQSCS, University of Leicester, University Road LE1 7RH, Leicester, UK

    Sandro Sozzo

Authors
  1. Diederik Aerts
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  2. Massimiliano Sassoli de Bianchi
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  3. Sandro Sozzo
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Correspondence to Sandro Sozzo.

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Aerts, D., de Bianchi, M.S. & Sozzo, S. The Extended Bloch Representation of Entanglement and Measurement in Quantum Mechanics. Int J Theor Phys 56, 3727–3739 (2017). https://doi.org/10.1007/s10773-016-3257-7

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  • DOI: https://doi.org/10.1007/s10773-016-3257-7

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