2007/11/30 by Łukasz Pańkowski, Łukasz Pankowski, Marco Piani +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Discrete mathematics #Mathematics #Matrix (chemical analysis) #Physics #Property (philosophy) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Rank (graph theory) #Simple (philosophy) #State (computer science) #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1109/tit.2010.2050810
published as IEEE Trans. Inf. Theory 56, 4085--4100 (2010) · 15 pages, Final version for IEEE Trans. Inf. Theory
arxiv created 2010/02/15 · openalex publication_date 2010/07/21 · arxiv updated 2010/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, existence of bound entangled states with nonpositive partial transpose (NPT) is considered. As one knows, existence of such states would in particular imply nonadditivity of distillable entanglement. Moreover, it would rule out a simple mathematical description of the set of distillable states. The particular state, known to be 1-copy nondistillable and supposed to be bound entangled, is considered. The problem of its two-copy distillability, which boils down to show that maximal overlap of some projectorQwith Schmidt rank two states does not exceed 1/2 (called thehalf-property), is studied. First, it is shown that the maximum overlap can be attained on vectors that are not of the simple product form with respect to cut between two copies. Then, the problem in attacked twofold way: (a) the half-property is proved for some wide classes of Schmidt rank two states; (b) the overlap forallSchmidt rank two states is bounded from above bycA⊗I+I⊗BwithA,Btraceless 4 × 4 matrices, and TrAfA+ TrBfB=1/4.