Entanglement Quantification via Symmetric Extensions: A Resource Theory Hierarchy

• URL: http://arxiv.org/abs/2607.16960v1
• Date: Sat, 18 Jul 2026 20:39:35 GMT
• Title: Entanglement Quantification via Symmetric Extensions: A Resource Theory Hierarchy
• Abstract summary: We introduce a hierarchy of entanglement measures Ek based on k-symmetric PPT extensions.<n>Each Ek, defined via a minimal eigenvalue shift, is faithful, convex, and monotone under free operations.<n>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.
• Score: 3.662037602213926
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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