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

TL;DR

This paper proposes analytic formulas for quantifying non-local magic in bipartite systems of prime local dimensions, supported by numerical evidence, and explores their limitations and relations to entanglement in higher dimensions.

Contribution

It introduces conjectured analytic expressions for non-local magic in bipartite qudit states and examines their accuracy and limitations across different dimensions.

Findings

Analytic formulas are supported by numerical evidence for qutrits and ququints.

Expressions approximate non-local magic but do not always find the global minimum in composite dimensions.

Relations between non-local magic and entanglement diagnostics do not extend to higher-dimensional systems.

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.