Analytic formulae for non-local nonstabiliserness in bipartite systems of qutrits and ququints

Abstract:We conjecture analytic expressions for the non-local magic of bipartite pure qudit states of prime local dimension. Our construction relies on the Schmidt-aligned state attaining the minimum over local unitaries, a hypothesis that we support with numerical evidence for pairs of qutrits and ququints. For composite local dimensions, we find that the analogous expressions do not in general reproduce the global minimum, but can still provide computationally cheap approximations to the non-local magic. We also find that relations between non-local magic and entanglement diagnostics that hold for two qubits generally do not extend to qutrit and higher-dimensional systems. As a few-body application, we evaluate the qutrit non-local magic generated by elastic pion scattering, treating hadronic isospin as the qutrit. We find that $p$-wave charged pion scattering realises the maximum non-local magic allowed in the system just below the $\rho$-meson resonance.

arXiv:2603.09155 [quant-ph]

(or arXiv:2603.09155v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.09155 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 114, 042414 (2026)

https://doi.org/10.1103/jh55-rmc6 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.