2005/04/27 by Sergey Bravyi, David Fattal, Daniel Gottesman · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1063/1.2203431
published as J. Math. Phys. 47 062106 (2006) · 12 pages, 1 figure
arxiv created 2005/04/27 · openalex publication_date 2006/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let ∣Ψ⟩ be an arbitrary stabilizer state distributed between three remote parties, such that each party holds several qubits. Let S be a stabilizer group of ∣Ψ⟩. We show that ∣Ψ⟩ can be converted by local unitaries into a collection of singlets, GHZ states, and local one-qubit states. The numbers of singlets and GHZs are determined by dimensions of certain subgroups of S. For an arbitrary number of parties m we find a formula for the maximal number of m-partite GHZ states that can be extracted from ∣Ψ⟩ by local unitaries. A connection with earlier introduced measures of multipartite correlations is made. An example of an undecomposable four-party stabilizer state with more than one qubit per party is given. These results are derived from a general theoretical framework that allows one to study interconversion of multipartite stabilizer states by local Clifford group operators. As a simple application, we study three-party entanglement in two-dimensional lattice models that can be exactly solved by the stabilizer formalism.