通过对称扩展进行纠缠量化：一种资源理论层次结构
Entanglement Quantification via Symmetric Extensions: A Resource Theory Hierarchy
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中文总结 AI 辅助
研究通过k对称PPT扩展引入纠缠度量Ek层次结构，其在自由操作下有良好性质，能检测束缚纠缠等，数值实验证明可扩展性，统一了计算效率与操作保真度，提供了处理所有纠缠态的资源理论尺度。
中文摘要 AI 辅助
我们引入了基于k对称PPT扩展的纠缠度量Ek层次结构。每个Ek通过最小特征值偏移定义并由半定规划计算，在自由操作下是忠实、凸且单调的。该层次结构在k = 1时严格细化PPT鲁棒性，在k = 2时检测束缚纠缠，当k趋于无穷时精确收敛到可分性度量。对多种态的数值实验证明了其实际可扩展性。我们的框架将计算效率与操作保真度统一在一个可调谐族中，首次提供了一个系统可改进的资源理论尺度来处理所有纠缠态。
英文摘要
We introduce a hierarchy of entanglement measures Ek based on k-symmetric PPT extensions. Each Ek, defined via a minimal eigenvalue shift and computed by semidefinite programming, is faithful, convex, and monotone under free operations. The hierarchy strictly refines PPT-robustness at k = 1, detects bound entanglement at k = 2, and converges exactly to the separability measure as k -> infinity. Numerical experiments on Horodecki, Werner, UPB, and random states demonstrate practical scalability. Our framework unifies computational efficiency with operational fidelity in a single tunable family -- a combination previously believed to be fundamentally incompatible in entanglement quantification. It supplies, for the first time, a systematically improvable resource-theoretic yardstick that accounts for all entangled states, including the bound entangled ones that have long resisted quantitative treatment.
