GHZ extraction yield for multipartite stabilizer states

Abstract

Let $|\Psi >$ be an arbitrary stabilizer state distributed between three remote parties, such that each party holds several qubits. Let $S$ be a stabilizer group of $|\Psi >$. We show that $|\Psi >$ 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 $|\Psi >$ 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.

12 pages, 1 figure

References in corpus (7)

• Quantum cryptography: Public key distribution and coin tossing
• Multi-party entanglement in graph states
• Unitarily localizable entanglement of Gaussian states
• Entanglement in the stabilizer formalism
• Local unitary versus local Clifford equivalence of stabilizer states
• BCS-like Modewise Entanglement of Fermion Gaussian States
• The invariants of the local Clifford group

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