2007/09/30 by Jonathan Walgate, A. J. Scott, A.J. Scott · 62 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Dimension (graph theory) #Discrete mathematics #Geometry #Hilbert space #Linear subspace #Mathematical analysis #Mathematics #Multipartite #Multipartite entanglement #Peres–Horodecki criterion #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum state #Separable space #Separable state #Squashed entanglement #Subspace topology #W state #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/37/375305
published in Journal of Physics A Mathematical and Theoretical 41(37), 375305 (Institute of Physics) · 12 pages
openalex publication_date 2008/08/13 · arxiv created 2008/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, smax, approaching the full dimension of the system, D. We show that almost all subspaces with dimension s = smax are completely entangled and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n = D - smax. This condition holds for almost all sets of states of all multipartite systems and reveals something surprising. The criterion is identical for separable and nonseparable states: entanglement makes no difference.