Quantum state tomography with muons

TL;DR

This paper proposes a method to observe quantum entanglement and Bell inequality violations in muon-electron scattering, enabling quantum tomography with muons across a wide energy range.

Contribution

It introduces a realistic approach and detailed analysis for detecting entanglement in muon-electron systems using relativistic quantum field theory.

Findings

High event rate allows observation of entanglement.

Bell inequality violations can be tested with muons.

Framework enables quantum tomography with muons.

Abstract

Entanglement is a fundamental pillar of quantum mechanics. Probing quantum entanglement and testing Bell inequality with muons can be a significant leap forward, as muon is arguably the only massive elementary particle that can be manipulated and detected over a wide range of energies, e.g., from approximately 0.3 to $10^2$ GeV, corresponding to velocities from 0.94 to nearly the speed of light. In this work, we present a realistic proposal and a comprehensive study of quantum entanglement in a state composed of different-flavor fermions in muon-electron scattering. The polarization density matrix for the muon-electron system is derived using a kinematic approach within the relativistic quantum field theory framework. Entanglement in the resulting muon-electron qubit system and the violation of Bell inequalities can be observed with a high event rate. This paves the way for performing quantum tomography with muons.