基于局域边际的混合态确定的秩与范围准则
Rank and Range Criteria for Mixed-State Determination from Local Marginals
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中文总结 AI 辅助
该研究针对量子系统认证的k-UDA问题，开发基于范围的方法，推导相关准则并将其应用于多体纠缠认证，明确了三量子比特态的UDA判定条件及高阶障碍。
中文摘要 AI 辅助
确定混合量子态是否在所有态中由其k体边际唯一确定（k-UDA）是量子系统认证中的基础问题。我们通过分析全局态的范围结构，开发了一种基于范围的方法来解决该问题。对于三量子比特态，我们证明具有无GHZ-SLOCC范围的态在秩为1、3、4时为2-UDA。我们推导了秩为2的2-UDA态的充要范围准则，并将其简化为有限二次型检验。为覆盖剩余的范围构型，我们提出了一种精确的范围受限半定规划准则，并将其扩展到任意有限维三分态。我们还证明每个秩至少为5的三量子比特态都不是2-UDA，并将高阶障碍扩展到多体系统。对于基于信道的多体系族，我们精确表征了态为(n-1)-UDA的情况，并表明低阶边际永远不足。最后，我们将这些结果应用于真正多体纠缠的认证。
英文摘要
Determining whether a mixed quantum state is uniquely determined among all states by its k-body marginals (k-UDA) is a fundamental problem in quantum system certification. We develop a range-based approach to this problem by analyzing the structure of the range of the global state. For three-qubit states, we show that states with GHZ-SLOCC-free ranges are 2-UDA at ranks one, three, and four. We derive a necessary and sufficient range criterion for rank-two 2-UDA states and reduce it to a finite quadratic-form test. To cover the remaining range configurations, we formulate an exact range-restricted semidefinite programming criterion and extend it to arbitrary finite-dimensional tripartite states. We also show that every three-qubit state of rank at least five is not 2-UDA, and further extend high-rank obstructions to multipartite systems. For a channel-based multipartite family, we characterize exactly when a state is $(n-1)$-UDA and show that lower-order marginals never suffice. Finally, we apply these results to the certification of genuine multipartite entanglement.
