2001/05/31 by Matthew J. Donald, Michał Horodecki, Michal Horodecki +1 · 206 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Convexity #Entropy (arrow of time) #Kullback–Leibler divergence #Mathematical analysis #Mathematics #Measure (data warehouse) #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Squashed entanglement #Statistics #Uniqueness #Von Neumann entropy #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.1495917
published in Journal of Mathematical Physics 43(9), 4252-4272 (American Institute of Physics) · 22 pages, LaTeX, version accepted by J. Math. Phys
arxiv created 2002/03/15 · openalex publication_date 2002/09/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We explore and develop the mathematics of the theory of entanglement measures. After a careful review and analysis of definitions, of preliminary results, and of connections between conditions on entanglement measures, we prove a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem on extreme entanglement measures in the case of mixed states. We analyze properties of the asymptotic regularization of entanglement measures proving, for example, convexity for the entanglement cost and for the regularized relative entropy of entangle ment.