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

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.

Are Collapse Models Testable via Flavor Oscillations?

“…[56]) one can straightforwardly obtain the full quantum information content of the meson systems, e.g. to study Heisenberg's uncertainty in relation with CP violation in the time evolution [57,58]. Let us focus our attention on the stochastic average, i.e.…”

A quantum information view on observables in the neutral kaon system

“…In a recent publication [1] an effective formalism was developed to express the quantum mechanical expectation value by effective time dependent operators in the reduced Hilbert-Schmidt space of the surviving component. This has the advantage that the Bell inequality can be formulated as a witness operator and for a given initial state the value of the Bell inequality can be simply derived.…”

“…The maximal uncertainty for the C P violation parameter δ = 3.322 · 10 −3 (world average [30]) is reached for t n = 11.4τ S (see also Ref. [1]). …”

“…time-dependent, and effectively living in the surviving part of the in general infinite dimensional Hilbert space which was recently introduced in Ref. [1].…”

Newtonian self-gravitation in the neutral meson system

“…For example, a violation of Bell's inequality that is only due to the breaking of a discrete symmetry resulting in a tiny difference between matter and antimatter properties has been discovered [21]. Or due to the existence of two distinct measurement procedures, a special feature of kaons, the very working of a quantum eraser [22,23] or Heisenbergs principle [24] can in a novel way be demonstrated. Proposals how to test decoherence effects have been developed [25,26] and put to experimental tests [27][28][29].…”