Interplay between classical and quantum signals: partial trace and measurement channels View Full Text


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Article Info

DATE

2010-11

AUTHORS

Andrei Khrennikov, Masanori Ohya, Naboru Watanabe

ABSTRACT

We continue the study of similarities between quantum information theory and theory of classical Gaussian signals. The possibility of using quantum entropy for classical Gaussian signals was explored a long time ago. Recently we demonstrated that some basic quantum channels can be represented as linear transforms of classical Gaussian signals. Here we consider bipartite quantum systems and show that an important quantum channel given by the partial trace operation has a simple classical representation, namely, a coordinate projection of a classical “prequantum signal.” We also consider the classical signal realization of quantum channels corresponding to state transforms in the process of measurement. The latter induces a difficult interpretational problem — the output signal corresponding to one system depends on a measurement that has been done on the second system. This situation might be interpreted as a sign of quantum nonlocality, action at a distance. Although we do not exclude such a possibility, i.e., that, in complete accordance with Bell, the creation of a realistic prequantum model is impossible without action at a distance, we found another interpretation of this situation that is not related to quantum nonlocality. More... »

PAGES

589-598

References to SciGraph publications

  • 2006-11. A probabilistic operator symbol framework for quantum information in JOURNAL OF RUSSIAN LASER RESEARCH
  • 2009-09. Quantum correlations from classical Gaussian correlations in JOURNAL OF RUSSIAN LASER RESEARCH
  • 2010-09. Classical signal model for quantum channels in JOURNAL OF RUSSIAN LASER RESEARCH
  • 2001-11. A Charged Particle in an Electric Field in the Probability Representation of Quantum Mechanics in JOURNAL OF RUSSIAN LASER RESEARCH
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  • 2009. Contextual Approach to Quantum Formalism in NONE
  • 2006-08. Prequantum Classical Statistical Field Theory: Complex Representation, Hamilton-Schrödinger Equation, and Interpretation of Stationary States in FOUNDATIONS OF PHYSICS LETTERS
  • 2008-01. Quantum Randomness as a Result of Random Fluctuations at the Planck Time Scale? in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 1986-06. A new treatment of communication processes with Gaussian channels in JAPAN JOURNAL OF APPLIED MATHEMATICS
  • 2007-06. Prequantum classical statistical field theory: Time scale of fluctuations in DOKLADY MATHEMATICS
  • 2005-12. Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory in FOUNDATIONS OF PHYSICS LETTERS
  • 1997. Information Dynamics and Open Systems, Classical and Quantum Approach in NONE
  • 2009-02. Bell’s inequality, Einstein, Podolsky, Rosen arguments and von Neumann’s projection postulate in LASER PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10946-010-9179-6

    DOI

    http://dx.doi.org/10.1007/s10946-010-9179-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1001329920


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