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Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism for unstable two-state systems

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Abstract

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of \(\mathcal{CP}\) violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.

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Authors and Affiliations

  1. Università degli Studi di Roma, La Sapienza, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Antonio Di Domenico

  2. INFN Sezione di Roma, Rome, Italy

    Antonio Di Domenico

  3. Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

    Andreas Gabriel, Beatrix C. Hiesmayr, Florian Hipp, Marcus Huber, Gerd Krizek, Karoline Mühlbacher, Sasa Radic & Christoph Spengler

  4. Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511, Bratislava, Slovakia

    Beatrix C. Hiesmayr & Lukas Theussl

Authors
  1. Antonio Di Domenico
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  2. Andreas Gabriel
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  3. Beatrix C. Hiesmayr
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  4. Florian Hipp
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  5. Marcus Huber
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  7. Karoline Mühlbacher
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  8. Sasa Radic
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  9. Christoph Spengler
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  10. Lukas Theussl
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Corresponding author

Correspondence to Beatrix C. Hiesmayr.

Additional information

Beatrix C. Hiesmayr wants to thank Gregor Weihs for the invitation to give a talk at the conference “Advances in Quantum Theory” (Växjö, Sweden, June 2010) and Andrei Khrennikov for inviting her to organize a session “Fundamentals of QM tested in High Energy Physics” in the forthcoming conference “Foundations of Probability and Physics-6” (Växjö, Sweden, 13–16 June 2010), which initiated this work.

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Di Domenico, A., Gabriel, A., Hiesmayr, B.C. et al. Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics. Found Phys 42, 778–802 (2012). https://doi.org/10.1007/s10701-011-9575-y

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  • DOI: https://doi.org/10.1007/s10701-011-9575-y

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