A hierarchy of representability conditions for 2-RDMs in non-particle-number-conserving quantum systems is obtained from the polar cone of the p-positive cone, unified with conserving cases by adding particle-number variance.
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Develops a systematic relaxation of ensemble N-representability for 1RDMs with partial information, solved via generalized Horn constraints plus weighted ensemble conditions, yielding a convex polytope for excited-state DFT.
Correlated purification via bi-objective semidefinite programming restores N-representability to noisy 2-RDMs from fermionic shadow tomography and achieves chemical accuracy on hydrogen chain dissociation curves.
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Refining ensemble $N$-representability of one-body density matrices from partial information
Develops a systematic relaxation of ensemble N-representability for 1RDMs with partial information, solved via generalized Horn constraints plus weighted ensemble conditions, yielding a convex polytope for excited-state DFT.