Representability for Quantum Theory beyond Particle-Number Conservation
Abstract
Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a solution of the representability problem for quantum systems without particle-number conservation. The physically allowed set of 2-RDMs can be characterized from a geometrically `orthogonal' set, the polar cone. We derive explicit linear equations for the two-body operators in the polar cone -- the intersection of the -positive cone with the two-body operator space -- to obtain a systematic hierarchy of representability conditions that do not depend on higher RDMs or the wave function. Moreover, by augmenting these conditions with the particle-number variance, we obtain a unified framework for treating both particle-number-conserving and nonconserving systems. We illustrate with a spin system and molecular H.
Cite
@article{arxiv.2604.23869,
title = {Representability for Quantum Theory beyond Particle-Number Conservation},
author = {David A. Mazziotti},
journal= {arXiv preprint arXiv:2604.23869},
year = {2026}
}