2016/09/30 by Gilad Gour, Barbara Kraus, Nolan R. Wallach
Computer Science · Mathematics · Physics and Astronomy · #Mathematics #Multipartite #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Stabilizer (aeronautics) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.5003015
published as Journal of Mathematical Physics 58, 092204 (2017) · 6 pages (main text) + 7 pages (Appendix), no figures, published version
openalex publication_date 2017/09/01 · arxiv created 2017/12/05 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The stabilizer group of an n-qubit state |ψ is the set of all matrices of the form g=g1⊗⋯⊗gn, with g1,…,gn being any 2 × 2 invertible complex matrices that satisfy g|ψ=|ψ. We show that for 5 or more qubits, except for a set of states of zero measure, the stabilizer group of multipartite entangled states is trivial, that is, containing only the identity element. We use this result to show that for 5 or more qubits, the action of deterministic local operations and classical communication (LOCC) can almost always be simulated simply by local unitary (LU) operations. This proves that almost all n-qubit states with n≥5 can neither be reached nor be converted into any other (n-partite entangled), LU-inequivalent state via deterministic LOCC. We also find a simple and elegant expression for the maximal probability to convert one multi-qubit entangled state to another for this generic set of states.