Quantum properties of heavy-fermion pairs at a lepton collider with polarised beams

TL;DR

This work develops a density-matrix framework to study quantum information aspects of heavy-fermion pair production $l\bar l\to F\bar F$ with polarised lepton beams, focusing on spin correlations, entanglement, Bell-inequality violation, purity, and stabiliser Rényi entropy. It derives analytic expressions for final-state spin density matrices in the presence of scalar, vector, and tensor EFT four-fermion operators and demonstrates that beam polarisation reveals a richer set of spin configurations and amplifies sensitivity to non-standard interactions. Through detailed analyses of $e^+e^-\to t\bar t$ in the SM and in EFT benchmarks, the paper shows how $\Gamma$, $\mathcal C$, $\mathcal B_{CHSH}$, and $M_2$ (in both helicity and beam bases) map distinctly onto operator structures and kinematics, enabling a powerful, multi-observable probe of new physics. It also shows that enforcing positivity of EFT-truncated density matrices can impose stronger constraints on the EFT scale than rate-based criteria, underscoring the value of quantum-information diagnostics as a consistency check for EFT analyses. Overall, the results advocate using polarised lepton colliders as quantum-information–driven laboratories for precision top-quark physics and indirect new-physics searches, with clear pathways for future refinements (NLO corrections, decays, tomography, and global EFT fits).

Abstract

We investigate the quantum properties of heavy-fermion pairs, such as $t\bar t$ or $τ^+τ^-$, produced in lepton-lepton collisions with polarised beams. Focusing on spin correlations, entanglement, Bell-inequality violation, and quantum-information--theoretic measures such as purity and magic, we analyse how beam polarisation shapes the structure of the spin-density matrix. We derive analytic expressions for a wide range of helicity configurations, including both Standard Model contributions and generic new-physics effects parametrised by scalar, vector, and tensor four-fermion operators within an effective field theory framework. We show that beam polarisation unlocks a substantially richer set of spin configurations and significantly enhances sensitivity to non-standard interactions. As a phenomenological application, we study $t\bar t$ production at a future linear collider and demonstrate that quantum observables provide a comprehensive and complementary probe of top-quark interactions and stronger constraints on the scale of new physics.

Figures (23)

• Figure 1: The purity $\Gamma$ (left), the Bell-CHSH observable ${\cal B}_{\rm CHSH}$ (middle) and the SRE in the beam-basis $M_2^{(\hat{z})}$ (right) are computed for the initial state $\rho^{\rm in}$ and shown in the $({\cal P}, \overline{\cal P})$ plane.
• Figure 2: The stabiliser Rényi entropies (SREs) for the scalar four-fermion interaction. The left panel shows the SRE in the helicity-basis, $M_2$, over the $(\eta_S, \beta)$ plane. The right panel shows the SRE in the beam-basis, $M_2^{(\hat{z})}$, over the $(\delta_S, \cos \Theta)$ plane.
• Figure 3: The left panel displays the purity $\Gamma$ for the vector interaction ($\sin \eta_A = 0$) over the ($\sin^2 \bar{\Phi} , \beta \sin \Theta$) plane. The right panel shows the concurrence ${\cal C}$ (blue) and the Bell-CHSH observable ${\cal B}_{\rm CHSH}$ (red) as functions of $\beta \sin\Theta$.
• Figure 4: The upper (lower) panel shows the helicity (beam) basis stabiliser Rényi entropy $M_2$ ($M_2^{(\hat{z})}$) for the vector-like case $(\sin \eta_A = 0)$ over the $(\sin^2 \bar{\Phi} , \cos \Theta)$ plane, respectively. The left, middle and right panels correspond to different velocities: $\beta = 0$ (threshold); $\beta = 0.8$ (intermediate); and $\beta = 1$ (ultra-relativistic). The upper-right plot also represents the $M_2$ for the axial-vector-like interaction ($\cos \eta_A = 0$).
• Figure 5: The beam-basis stabiliser Rényi entropy $M_2^{(\hat{z})}$ for the axial-vector-like interaction ($\cos \eta_A = 0$) presented over the $(\sin^2 \bar{\Phi} , \cos \Theta)$ plane.