2008/02/27 by Caterina Mora, Caterina-E Mora, Marco Piani +2 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Wireless Communication Security Techniques #quant-ph
paper · pdf · doi:10.1088/1367-2630/10/8/083027
published as 2008 New J. Phys. 10 083027 (15pp) · 9 pages, 3 figures
arxiv created 2008/02/27 · openalex publication_date 2008/08/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We associate to every entanglement measure a family of measures which depend on a precision parameter, and which we call epsilon-measures of entanglement. Their definition aims at addressing a realistic scenario in which we need to estimate the amount of entanglement in a state that is only partially known. We show that many properties of the original measure are inherited by the family, in particular weak monotonicity under transformations applied by means of Local Operations and Classical Communication (LOCC). On the other hand, they may increase on average under stochastic LOCC. Remarkably, the epsilon-version of a convex entanglement measure is continuous even if the original entanglement measure is not, so that the epsilon-version of an entanglement measure may be actually considered a smoothed version of it.