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

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 $e^+ e^- \to t\bar{t},\ e^+e^-\to μ^+μ^-$ 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 Rényi 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 $5σ$ 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.

💡 Research Summary

This paper presents a comprehensive quantum‑tomography analysis of fermion‑pair production at prospective electron‑positron colliders, focusing on how longitudinal beam polarization manipulates the two‑qubit spin density matrix. The authors examine three benchmark processes: (i) $e^+e^-\to t\bar t$, representing a threshold‑dominated, massive‑quark system; (ii) $e^+e^-\to\mu^+\mu^-$, a light‑lepton pair produced at the $Z$‑pole where the $s$‑channel dominates; and (iii) Bhabha scattering $e^+e^-\to e^+e^-$, which features a non‑trivial interplay of $s$‑ and $t$‑channel amplitudes.

The theoretical framework relies on the Fano‑Bloch decomposition of the two‑qubit density matrix, \