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

• URL: http://arxiv.org/abs/2607.26122v1
• Date: Tue, 28 Jul 2026 18:00:00 GMT
• Title: Qubit-qubit-qutrit quantum correlations in $H \to f \bar f V$
• Abstract summary: We analyse the 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.<n>We derive expressions for the tight $4 times 4 times 2$ Bell inequalities of the $2 otimes 2 otimes 3$ system.<n>We extend the stabiliser Rényi entropy and the non-local magic to systems with unequal local dimensions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $h \to τ^- τ^+ Z$. 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.

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