Full local-unitary optimization of nonlocal magic measures

Determine the full local-unitary optimizers of the nonlocal stabilizer Rényi entropy, stabilizer extent, generalized robustness, and mana, in order to establish how far the sorted computational-basis geometry extends beyond the stabilizer fidelity.

Background

The paper exactly solves the local-unitary optimization defining nonlocal magic for the stabilizer fidelity, showing that an ordered computational-basis representative of the Schmidt decomposition is globally optimal. It also derives bounds relating the resulting nonlocal min-relative entropy of nonstabilizerness to the nonlocal stabilizer Rényi entropy, stabilizer extent, and generalized robustness.

The corresponding optimizing local unitaries for those other measures, as well as for mana, are not determined. Solving these optimization problems would reveal whether the spectral and sorted-basis structure identified for stabilizer fidelity persists for broader classes of nonlocal magic measures.