Quantum Tomography of Fermion Pairs in $e^+e^-$ Collisions: Longitudinal Beam Polarization Effects

TL;DR

This paper investigates how longitudinal beam polarization at future $e^+e^-$ colliders influences quantum properties like entanglement, nonlocality, and non-stabilizerness in fermion pair production, highlighting potential for quantum-information studies in high energy physics.

Contribution

It introduces a quantum tomography framework for fermion pairs at colliders, analyzing polarization effects on quantum resources and demonstrating experimental observability of quantum phenomena.

Findings

Polarization reshapes single-spin polarizations in $s$-channel channels.

Entanglement and Bell nonlocality are robust against polarization changes.

Quantum resources can be observed with high significance in collider experiments.

Abstract

We present a quantum tomography study of fermion pair production at future $e^+e^-$ colliders, emphasizing how longitudinal beam polarization controls the two-qubit spin density matrix. We study the processes $e^+ e^- \to t\bar{t},\ e^+e^-\to \mu^+\mu^-$ and Bhabha scattering $e^+e^-\to e^+e^-$, representing the mass threshold behavior, the $Z$ pole resonance and the $s/t$-channel interplay. We choose to focus on three key concepts: quantum entanglement via the concurrence $\mathcal{C}$, Bell nonlocality via the optimal Clauser Horne Shimony Holt (CHSH) parameter $\mathcal{B}$, and non-stabilizerness (``magic'') via the second stabilizer R\'enyi entropy $\mathcal{M}_2$. For the $s$-channel-dominated channels, longitudinal polarization mainly reshapes single-spin polarizations while leaving the spin-correlation matrix largely unchanged, rendering $\mathcal{C}$ and $\mathcal{B}$ comparatively robust, but inducing a pronounced variation of $\mathcal{M}_2$. In contrast, in Bhabha scattering, polarization modifies the relative contributions of the $s$-channel and $t$-channel and can strongly affect all three observables. The observability of entanglement, Bell nonlocality, and magic exceeds the $5\sigma$ level when both statistical and systematic uncertainties are included, establishing the fermion pair systems as ideal laboratories for quantum-information studies in high energy leptonic collisions. With optimized beam polarization, future $e^+e^-$ colliders will provide a unique opportunity to experimentally explore and influence quantum resources in particle interactions.