2006/03/31 by L. Lamata, Lucas Lamata, J. Leon +4 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Basis (linear algebra) #Class (philosophy) #Computer science #Data mining #Discrete mathematics #LOCC #Mathematics #Measure (data warehouse) #Multipartite #Multipartite entanglement #Physics #Product (mathematics) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Squashed entanglement #State (computer science) #Statistical physics #W state #quant-ph
paper · pdf · doi:10.1103/physreva.74.052336
published as Phys. Rev. A 74, 052336 (2006) · 11 pages and no figures. Accepted in PRA
arxiv created 2006/10/27 · openalex publication_date 2006/11/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We propose an inductive procedure to classify N-partite entanglement under stochastic local operations and classical communication provided such a classification is known for N\ensuremath-1 qubits. The method is based upon the analysis of the coefficient matrix of the state in an arbitrary product basis. We illustrate this approach in detail with the well-known bipartite and tripartite systems, obtaining as a by-product a systematic criterion to establish the entanglement class of a given pure state without resourcing to any entanglement measure. The general case is proved by induction, allowing us to find an upper bound for the number of N-partite entanglement classes in terms of the number of entanglement classes for N\ensuremath-1 qubits.