Fermionic Gaussian Scrooge ensemble with a general Gaussian density matrix

Characterize a maximally random ensemble of fermionic Gaussian states with a general Gaussian density matrix using only information from the subsystem under consideration, thereby providing the appropriate universal target ensemble for projected ensembles generated by free-fermion evolutions.

Background

Free-fermion dynamics preserves Gaussianity, so projected post-measurement states occupy the constrained manifold of fermionic Gaussian states rather than the full Hilbert space. The paper explains that existing studies had considered either the featureless Gaussian Haar ensemble or target ensembles requiring information about the entire system.

A maximally random fermionic Gaussian ensemble determined by a general Gaussian density matrix and subsystem information would provide the analogue of the conventional Scrooge ensemble for free fermions. The paper subsequently introduces the fermionic Gaussian Scrooge ensemble to address this previously unexplored problem, so the passage identifies the motivating unresolved issue rather than an additional problem left unresolved by the paper's results.

References

A maximally random ensemble of fermionic Gaussian states with a general Gaussian density matrix, defined using only subsystem information, remains unexplored.

— Fermionic Gaussian Scrooge Ensembles in Deep Thermalization  (2610.01209 - Sun et al., 1 Oct 2026) in Introduction

As discussed in , in this scenario, the pure states of $A$ in the projected ensemble are conjectured to be drawn from the uniform, maximally entropic manifold of states.

— Gaussian Scrooge Ensemble from Deep Thermalization in Free-Fermions  (2610.10279 - Russotto et al., 7 Oct 2026) in Section 4.1, 'Effective non-revelation of local conserved charges'