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

TL;DR

This paper develops a formalism to analyze decaying two-state systems in high energy physics, applying quantum information concepts like uncertainty relations and Bell inequalities to oscillating meson-antimeson systems, including CP violation effects.

Contribution

It introduces an operator formalism for decaying systems, enabling the application of quantum information tools like Bell inequalities and uncertainty relations in high energy physics.

Findings

Entropic Heisenberg uncertainty relation derived for meson systems

Operator-form Bell inequalities applicable to unstable particles

Analysis includes effects of CP violation in high energy systems

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 feature 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 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.