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GHZ extraction yield for multipartite stabilizer states

Bravyi, Sergey and Fattal, David and Gottesman, Daniel (2006) GHZ extraction yield for multipartite stabilizer states. Journal of Mathematical Physics, 47 (6). Art. No. 062106. ISSN 0022-2488. doi:10.1063/1.2203431.

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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.

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Additional Information:©2006 American Institute of Physics (Received 20 January 2006; accepted 17 April 2006; published online 26 June 2006) The authors acknowledge Ike Chuang for fruitful discussion. One of the authors (S.B.) received support from the National Science Foundation under Grant No. EIA-0086038. One of the authors (D.G.) is supported by CIAR and by NSERC of Canada.
Subject Keywords:quantum computing; quantum entanglement; mathematical operators; group theory
Issue or Number:6
Record Number:CaltechAUTHORS:BRAjmp06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4578
Deposited By: Archive Administrator
Deposited On:29 Aug 2006
Last Modified:08 Nov 2021 20:18

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