2011/08/31 by Kil-Chan Ha, Seung-Hyeok Kye · 36 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Entanglement witness #Indecomposable module #Matrix (chemical analysis) #Quantum Information and Cryptography #Quantum entanglement #Set (abstract data type) #Spectral Theory in Mathematical Physics #State (computer science) #math-ph #math.MP #math.OA #msc:15A30 #msc:46L05 #msc:81P15 #quant-ph
paper · pdf · doi:10.1142/s1230161211000224
published in Open Systems & Information Dynamics 18(04), 323-337 (World Scientific) · 16 pages, Some typos are corrected
openalex publication_date 2011/12/01 · arxiv created 2012/01/07 · arxiv updated 2012/01/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider entanglement witnesses arising from positive linear maps which generate exposed extremal rays. We show that every entangled state can be detected by one of these witnesses, and this witness detects a unique set of entangled states among those. Therefore, they provide a minimal set of witnesses to detect any kind of entanglement in a sense. Furthermore, if those maps are indecomposable then they detect large classes of entangled states with positive partial transposes which have nonempty relative interiors in the cone generated by all PPT states. We also provide a one-parameter family of indecomposable positive linear maps which generate exposed extremal rays. This gives the first examples of such maps in three-dimensional matrix algebra.