Entanglement Quantification via Symmetric Extensions: A Resource Theory Hierarchy

Abstract: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.

arXiv:2607.16960 [quant-ph]

(or arXiv:2607.16960v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.16960 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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