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 http://resolver.caltech.edu/CaltechAUTHORS:BRAjmp06
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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.
|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|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||29 Aug 2006|
|Last Modified:||26 Dec 2012 09:00|
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