Foundations of Physics

, Volume 42, Issue 6, pp 778–802 | Cite as

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

An effective formalism for unstable two-state systems
  • Antonio Di Domenico
  • Andreas Gabriel
  • Beatrix C. HiesmayrEmail author
  • Florian Hipp
  • Marcus Huber
  • Gerd Krizek
  • Karoline Mühlbacher
  • Sasa Radic
  • Christoph Spengler
  • Lukas Theussl


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.


Meson–antimeson systems Bell inequalities Heisenberg’s uncertainty relation Entropy 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Antonio Di Domenico
    • 1
    • 2
  • Andreas Gabriel
    • 3
  • Beatrix C. Hiesmayr
    • 3
    • 4
    Email author
  • Florian Hipp
    • 3
  • Marcus Huber
    • 3
  • Gerd Krizek
    • 3
  • Karoline Mühlbacher
    • 3
  • Sasa Radic
    • 3
  • Christoph Spengler
    • 3
  • Lukas Theussl
    • 4
  1. 1.Università degli Studi di Roma, La SapienzaRomeItaly
  2. 2.INFN Sezione di RomaRomeItaly
  3. 3.Faculty of PhysicsUniversity of ViennaViennaAustria
  4. 4.Research Center for Quantum Information, Institute of PhysicsSlovak Academy of SciencesBratislavaSlovakia

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