Polarization, Maximal Concurrence, and Pure States in High-Energy Collisions

TL;DR

This paper derives a quantitative relationship between local spin polarization and quantum entanglement in two-qubit systems, showing how polarization limits entanglement and identifying conditions for maximum concurrence.

Contribution

It introduces a process-independent framework linking local polarization, maximal entanglement, and pure states, with an application to high-energy particle collisions.

Findings

Maximum concurrence is constrained by local polarization levels.

Pure states saturate the derived entanglement bounds in certain cases.

In specific kinematic regions, maximal entanglement is achieved and reduced by polarization.

Abstract

We establish a quantitative relation between local spin polarization and quantum entanglement in two-qubit systems by deriving an upper bound on the concurrence at fixed local polarization, showing that increasing polarization constrains the maximum achievable entanglement. We further demonstrate that this bound is saturated by pure states in certain cases. As a concrete physical application, we consider the parity-violating process $e^+e^- \to Z^0 \to q\bar{q}$, which generates final-state spin polarization. We show that the maximal concurrence is attained in specific kinematic regions and is significantly reduced relative to the unpolarized case. These results establish a general, process-independent framework connecting local polarization, maximal entanglement, and the role of pure states.