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

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 polarizations, showing that increasing polarization constrains the maximum achievable entanglement. We further demonstrate that this bound is saturated by pure states in certain cases with identical polarizations. 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.