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

Foundations of Physics 42 (6):778-802 (2012)

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
Keywords Meson–antimeson systems  Bell inequalities  Heisenberg’s uncertainty relation  Entropy
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DOI 10.1007/s10701-011-9575-y
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