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Typical entanglement of stabilizer states

Smith, Graeme and Leung, Debbie (2006) Typical entanglement of stabilizer states. Physical Review A, 74 (6). Art. No. 062314. ISSN 1050-2947. https://resolver.caltech.edu/CaltechAUTHORS:SMIpra06

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Abstract

How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large, the state will be close to maximally entangled with probability exponentially close to 1. We provide a similar tight characterization of the entanglement present in the maximally mixed state of a randomly chosen stabilizer code. Finally, we show that typically very few Greenberger-Horne-Zeilinger states can be extracted from a random multipartite stabilizer state via local unitary operations. Our main tool is a concentration inequality which bounds deviations from the mean of random variables which are naturally defined on the Clifford group.


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https://doi.org/10.1103/PhysRevA.74.062314DOIUNSPECIFIED
Additional Information:©2006 The American Physical Society. (Received 26 May 2006; published 20 December 2006) It is a pleasure to thank Patrick Hayden for both suggesting the line of inquiry we have pursued and providing useful comments along the way. We are also grateful to Sergey Bravyi for several essential discussions about entanglement in the stabilizer formalism, to Ben Toner for comments on an earlier draft of this paper, and to the participants in the Bellairs Workshop on Pseudo-Random Unitary Operators for many helpful comments and suggestions. We acknowledge the support of the U.S. National Science Foundation under Grant No. EIA-0086038, as well as NSERC of Canada. D.L. further acknowledges funding from the Tolman Foundation, CIAR, NSERC, CRC, CFI, and OIT.
Subject Keywords:quantum entanglement; quantum computing
Issue or Number:6
Record Number:CaltechAUTHORS:SMIpra06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:SMIpra06
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7278
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:25 Jan 2007
Last Modified:02 Oct 2019 23:40

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