Typical MRE at fixed particle number

Determine the typical magic Rényi entropy of fermionic states at fixed particle number, in order to characterize how particle-number conservation constrains non-Gaussianity and to establish a benchmark for the dynamics of such states.

Background

The main Haar-random-state analysis is performed in a fixed fermion-parity sector rather than at fixed particle number. Consequently, the typical MRE under particle-number conservation remains unresolved. Solving this problem would clarify the effect of an important physical symmetry constraint and provide a reference value against which particle-number-conserving many-body dynamics could be compared.