2000/06/29 by Koenraad M. R. Audenaert, K. Audenaert, Frank Verstraete +3 · 182 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Bipartite graph #Characterization (materials science) #Combinatorics #Function (biology) #Manifold (fluid mechanics) #Mathematical analysis #Mathematical optimization #Mathematics #Minification #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Separable space #Separable state #Unitary state #quant-ph
paper · pdf · doi:10.1103/physreva.64.052304
published in Physical Review A 64(5) (American Physical Society) · 11 pages RevTeX, 4 figures
arxiv created 2000/06/29 · openalex publication_date 2001/10/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we develop a mathematical framework for the characterization of separability and entanglement of formation (EOF) of general bipartite states. These characterizations are variational in nature, meaning that separability and EOF are given in terms of a function that is to be minimized over the manifold of unitary matrices. A major benefit of such a characterization is that it directly leads to a numerical procedure for calculating EOF. We present an efficient minimization algorithm and apply it to the bound entangled 3\ifmmode×\else\texttimes\fi3 Horodecki states; we show that their EOF is very low and that their distance to the set of separable states is also very small. Within the same variational framework we rephrase the results by Wootters [W. Wootters, Phys. Rev. Lett. 80, 2245 (1998)] on EOF for 2\ifmmode×\else\texttimes\fi2 states and also present some progress in generalizing these results to higher-dimensional systems.