2011/06/30 by Bang-Hai Wang, Dongyang Long, Dong-Yang Long · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Conjecture #Eigenvalues and eigenvectors #Entanglement witness #Identity matrix #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Separable space #Separable state #Sigma #Squashed entanglement #quant-ph
paper · pdf · doi:10.1103/physreva.87.062324
published as Phys. Rev. A 87, 062324 (2013) · 7 pages, fixed some typos, thanks to the many comments received!
openalex publication_date 2013/06/21 · arxiv created 2013/07/21 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The structural physical approximation (SPA) to a positive map is considered to be one of the most important methods to detect entanglement in the real physical world. We first show that an arbitrary entanglement witness (EW) W can be constructed from a separable density matrix \ensuremathσ in the form of W=\ensuremathσ\ensuremath-c_\ensuremathσI, where c_\ensuremathσ is a non-negative number and I is the identity matrix. Following the general form of EWs from separable states, we show a sufficient condition and a sufficient and necessary condition in low dimensions of that SPAs to positive maps do not define entanglement-breaking channels. We show that either the SPA of an EW or the SPA of the partial transposition of the EW in low dimensions is an entanglement-breaking channel. We give sufficient conditions of violating the SPA conjecture [Phys. Rev. A 78, 062105 (2008)]. Our results indicate that the SPA conjecture is independent of whether or not positive maps are optimal.