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arXiv · 2512.20133

Mixed States Uniquely Determined by Marginals and Additivity

Xinyu Qiu·Lin Chen·Genwei Li·Delin Chu
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Abstract

Identifying whether a mixed quantum state is uniquely determined among all states (UDA) by its local marginals is a basic problem in quantum information theory. We establish necessary and sufficient conditions under which several classes of multipartite mixed states are UDA by their $k$-partite marginals. We also prove structural properties based on ranges and marginals, and formulate a recursive procedure for the determination of UDA states. We show that sufficiently high rank rules out unique determination from fixed-order marginals, implying that almost all multipartite mixed states are not UDA from such marginals. Finally, we completely characterize the additivity of bipartite UDA states, three-qubit and several families of $n$-qubit product UDA states. These results clarify the boundary between UDA and non-UDA mixed states and provide a framework for local-marginal reconstruction and related certification tasks.

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Xinyu Qiu, Lin Chen, Genwei Li, Delin Chu. 2025-12-23. Mixed States Uniquely Determined by Marginals and Additivity. https://doi.org/10.1109/tit.2026.3699321

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