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

TL;DR

The paper addresses the lack of a general framework for collider spin-density matrices by integrating an automated production-density-matrix workflow into MadGraph5_aMC@NLO, producing event-by-event density matrices $\rho = R/\mathrm{Tr}[R]$ from helicity amplitudes $\mathcal{M}$ and embedding them in LHE files for post-processing of quantum observables. It introduces a companion Python library to compute local and bilateral polarisations, spin correlations, and a broad suite of quantum-information measures, including purity, concurrence, entanglement of formation, PPT/negativity, D-coefficients, and higher-spin generalisations such as magic and mana, across qubit-qubit, qubit-qutrit, and qutrit-qutrit systems. The framework is validated against established SM and BSM results for $t\bar{t}$ and $VV$ production at hadron and lepton colliders and in heavy-resonance decays, demonstrating high-precision agreement and robust phase-space coverage. It further showcases novel applications to $t\bar{t}W^{\pm}$, $tW^{\,-}$ vs $t(\bar{t}\to W^-\bar{b})$, and $t\bar{t}t$ vs $t\bar{t}t\bar{t}$ final states, illustrating how per-event density matrices enable systematic exploration of quantum correlations, frame- and basis-dependent diagnostics, and potential discrimination between SM and BSM dynamics. Overall, the tool links precise amplitude calculations with quantum-information diagnostics, providing a scalable platform for precision SM tests and BSM searches through spin coherence and entanglement phenomena at current and future colliders.

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: $t\bar t W^\pm$, $tW^-$ vs.\ $t(\bar t\to W^- \bar b)$, and $t\bar t t$ vs. $t\bar t t\bar t$.

Figures (33)

• Figure 1: Diagrams for $g\;g \to t \;\bar{t}$ at LO in QCD.
• Figure 2: Diagram for $q\;\bar{q} \to t \;\bar{t}$ at LO in QCD.
• Figure 3: Concurrence as a function of $\theta$ (\ref{['eq: theta1']}) and $\beta$ (\ref{['eq: beta_ttbar']}), in the centre-of-mass of the pair $t \bar{t}$ for the process $gg \to t\bar{t}$ at $\sqrt{s} = 13$ TeV. (a) (b) simulation results. The coarse graining on the right is related to the available statistics in the corresponding phase space region (1M of unweighted events).
• Figure 4: Same as Fig. \ref{['fig: Concurrence g g > t tbar']} for the $q \bar{q} \to t\bar{t}$ production channel.
• Figure 5: Concurrence (\ref{['pp-a']}) and cross-section (\ref{['pp-c']}) as a function of the production angle $\theta$ (\ref{['eq: theta1']}) and of $M_{t\bar{t}}$ in the centre-of-mass of the pair $t \bar{t}$ at the LHC ($p\; p$ at $\sqrt{s} = 13$ TeV). They can be compared with those obtained analytically, see Fig. 5 of Ref. 2003.02280.