Automated computation of spin-density matrices and quantum observables for collider physics

Abstract

We present a fully automated framework to compute production spin-density matrices for generic collider processes at tree level within \textsc{MadGraph5\_aMC@NLO}. The method assembles helicity amplitudes into event-by-event production matrices. These are written to the LHE file in a compact form, together with run metadata, enabling direct post-processing of quantum observables. The implementation supports bi- and multipartite qubit and qutrit final states, configurable reference frames, and both polarised and unpolarised initial states. A companion, easy-to-extend library provides analysis routines to determine key quantum-information measures and witnesses. These include purity, concurrence, and entanglement of formation for qubits; Peres--Horodecki tests and negativity; spin-polarisation vectors and correlation matrices; $D$-coefficients; and stabiliser-based ``magic'' measures. As a result, multi-particle quantum correlations can be quantified systematically. We validate the implementation against known results for $t\bar{t}$ and $VV$ ($V=W^{\pm },Z$) production in $pp$ and $e^{+}{e}^{-}$ collisions and in heavy-resonance decays. We then consider new applications and study quantum correlations in several LHC final states: $t\bar{t}{W}^{\pm }$, $t{W}^{-}$ vs.\ $t(\bar{t}\to W^{-}\bar{b})$, and $t\bar{t}t$ vs. $t\bar{t}t\bar{t}$.