由边缘唯一确定的混合态与可加性
Mixed States Uniquely Determined by Marginals and Additivity
AI总结：
研究混合量子态是否由其局部边缘唯一确定（UDA）的条件，建立了多体混合态为k-体边缘UDA的充要条件，并证明了基于范围和边缘的结构性质，给出了递归判定方法。
摘要：
识别混合量子态是否由其局部边缘在所有态中唯一确定（UDA）是量子信息论中的一个基本问题。我们建立了若干类多体混合态由其$k$-体边缘为UDA的充分必要条件。我们还证明了基于范围和边缘的结构性质，并制定了确定UDA态的递归程序。我们表明，足够高的秩排除了由固定阶边缘的唯一确定，这意味着几乎所有多体混合态都不是由这些边缘UDA的。最后，我们完全刻画了二体UDA态、三量子比特以及若干族$n$量子比特乘积UDA态的可加性。这些结果澄清了UDA与非UDA混合态之间的界限，并为局部边缘重建及相关认证任务提供了框架。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
