Unitarity constrains the quantum information metrics for particle interactions

TL;DR

This paper demonstrates how unitarity constrains quantum information metrics in particle interactions, enabling calculations of entanglement entropy, cross sections, and momentum entropy using quantum mechanics without traditional scattering amplitude methods.

Contribution

It introduces a novel approach using non-relativistic and relativistic quantum mechanics to derive key quantities like cross sections and entropy directly from unitarity constraints.

Findings

Derived density matrix for hard scattering without scattering amplitude

Calculated cross sections using quantum mechanics and unitarity

Connected entropy concepts with the uncertainty principle in scattering

Abstract

Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires the same von Neumann entanglement entropy generation for either a particle interaction or an act of measurement. For the first time, the language of non-relativistic quantum mechanics is presented to derive the density matrix for hard scattering. We show that unitarity allows for finding the latter's cross section without using the scattering amplitude or the Lippmann-Schwinger equation plus Green's function. We also show the language of relativistic quantum mechanics can be used to derive the momentum entropy or Sackur-Tetrode equation for the inelastic scattering of an electron from a proton. The latter entropy derives from a Shannon entropy and an additional entropy that evokes the uncertainty principle. This article's presentation allows particle physicists to readily begin calculating quantum information metrics such as correlations and mutual information for any particle interaction.