Characterize the admissible coherence hierarchy

Characterize the physically admissible domain of the hierarchy of electronic coherences $mathcal{G}^{(n)}$, including systematic necessary conditions beyond practical Cauchy–Schwarz inequalities and the full $N$-representability conditions required for consistency with a many-body reduced density operator.

Background

The tomography reconstruction is an inverse problem whose regularization depends on identifying which reconstructed coherences can arise from a physically acceptable many-body density operator. At the two-electron level, this admissibility is governed not only by positivity but also by the computationally difficult $N$-representability problem.

The paper derives explicit necessary two-electron constraints in an appendix, but does not develop a systematic treatment applicable across the entire hierarchy of electronic coherences. Such a study is explicitly left for future work.