Tightness of the finite-size universal MRE bound

Determine whether the universal upper bound on the magic Rényi entropy, M_2(\psi)\leq N\ln(4/3)-\ln(16/9), is tight for finite even system sizes.

Background

The paper proves a universal upper bound on the two-copy magic Rényi entropy (MRE) of every fixed-parity pure fermionic state. In the large-system limit, the bound establishes the maximal possible MRE density, but it does not determine whether the finite-size constant is attainable. Resolving this question would characterize the exact finite-N maximum of the MRE rather than only its asymptotic density.

References

Whether the bound is tight at finite $N$ remains open.

— Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity  (2610.02075 - Hoshino et al., 1 Oct 2026) in Main text, subsection “Universal upper bound on the MRE”