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

A bstract We present a fully automated framework to compute production spin-density matrices for generic collider processes at tree level within M a dG raph 5_ a MC@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 $$ t\overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and VV ( V = W ± , 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: $$ t\overline{t}{W}^{\pm } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:math> , tW − vs. $$ t\left(\overline{t}\to {W}^{-}\overline{b}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:mfenced> </mml:math> , and $$ t\overline{t}t $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>t</mml:mi> </mml:math> vs. $$ t\overline{t}t\overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> .