Remarks on the Equivalence of Full Additivity and Monotonicity for the Entanglement Cost

2007/02/28 by Fernando G. S. L. Brandao, F. G. S. L. Brandão, M. Horodecki +5 · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Additive function #Equivalence (formal languages) #Kullback–Leibler divergence #Mathematical Inequalities and Applications #Monotonic function #Multipartite entanglement #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #quant-ph

paper · pdf · doi:10.1007/s11080-007-9056-0

published in Open Systems & Information Dynamics 14(03), 333-339 (World Scientific) · 3 and a bit sides

openalex publication_date 2007/09/01 · arxiv created 2013/08/27 · arxiv updated 2013/08/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We analyse the relationship between the full additivity of the entanglement cost and its full monotonicity under local operations and classical communication. We show that the two properties are equivalent for the entanglement cost. The proof works for the regularization of any convex, subadditive, and asymptotically continuous entanglement monotone, and hence also applies to the asymptotic relative entropy of entanglement.

Citations

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Remarks on entanglement measures and non-local state distinguishability
• Asymptotic Relative Entropy of Entanglement