2006/11/25 by M. A. Jafarizadeh, G. Najarbashi, Hessam Habibian +1
Computer Science · Mathematics · Physics and Astronomy · #Class (philosophy) #Combinatorics #Computer science #Dimension (graph theory) #Discrete mathematics #Eigenvalues and eigenvectors #Geometry #Hilbert space #Mathematics #Mechanical and Optical Resonators #Multipartite #Multipartite entanglement #Physics #Pure mathematics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Reduction (mathematics) #Squashed entanglement #quant-ph
paper · pdf · doi:10.1103/physreva.75.052326
29 pages, 4 figures
arxiv created 2006/11/25 · openalex publication_date 2007/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A class of entanglement witnesses (EWs) called reduction-type entanglement witnesses is introduced, which can detect some multipartite entangled states including positive partial transpose ones with Hilbert space of dimension d1\ensuremath\bigotimesd2\ensuremath\bigotimes\ensuremath⋯\ensuremath\bigotimesdn. In fact the feasible regions of these EWs turn out to be convex polygons and hence the manipulation of them reduces to linear programming which can be solved exactly by using the simplex method. The decomposability and nondecomposability of these EWs are studied and it is shown that it has a close connection with eigenvalues and optimality of EWs. Also using the Jamio\lkowski isomorphism, the corresponding possible positive maps, including the generalized reduction maps of Hall [Phys. Rev. A 72, 022311 (2005)] are obtained.