Qubit-qubit-qutrit quantum correlations in $H\to f\bar{f}V$

Abstract

We perform an extensive analysis of the quantum correlations carried by the qubit-qubit-qutrit pure state arising in the decay of a massive scalar into a fermion-antifermion pair and a massive gauge boson, $H\to f\bar{f}V$, specialising to the Higgs boson decay $h\to {\tau }^{-}{\tau }^{+}Z$. Working with the exact tree-level spin state and its systematic expansion around the massless-fermion limit, we obtain analytic control over the entire phase space: the bipartite entanglement measures, the genuine $2\otimes 2\otimes 3$ entanglement structure (the Miyake classification), as well as the Bell-inequality violations and the non-stabiliserness (magic) are all mapped and reproduced by compact formulas. The bipartite measures exhibit a monogamy-like trade-off between the fermion pair and the fermion-boson pairs. The state is genuinely $2\otimes 2\otimes 3$ entangled over almost the entire phase space, most strongly in the collinear regions. We derive, for the first time, semi-analytical expressions for the tight $4\times 4\times 2$ Bell inequalities of the $2\otimes 2\otimes 3$ system, generalising the optimisation previously available only for three qubits, and find that the local-hidden-variable bound is violated over the entire phase space, reaching within a few per cent of the quantum bound at the upper endpoint of the di-tau mass spectrum. We further extend the stabiliser Rényi entropy and the non-local magic to systems with unequal local dimensions, and show that the near-endpoint state carries almost exactly one bit of non-local magic, which peaks at ${\log }_2\frac{27}{7}\simeq 1.95$ in the collinear regions. The differential decay rate concentrates precisely in the most nonclassical region of the phase space.

Comments: 49 pages, 13 figures