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Superselection rules and quantum protocols

Kitaev, Alexei and Mayers, Dominic and Preskill, John (2004) Superselection rules and quantum protocols. Physical Review A, 69 (5). Art2. No. 052326. ISSN 1050-2947. doi:10.1103/PhysRevA.69.052326.

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We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system—in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference system with suitable properties. By this method, we prove that if an n-party protocol is secure in a world subject to a superselection rule, then the security is maintained even if the superselection rule is relaxed. However, the proof applies only to a limited class of superselection rules, those in which the superselection sectors are labeled by unitary irreducible representations of a compact symmetry group. The second method uses the concept of the format of a message sent between parties—by verifying the format, the recipient of a message can check whether the message could have been sent by a party who performed charge-conserving operations. By this method, we prove that protocols subject to general superselection rules (including those pertaining to non-Abelian anyons in two dimensions) are no more secure than protocols in the unrestricted world. However, the proof applies only to two-party protocols. Our results show in particular that, if no assumptions are made about the computational power of the cheater, then secure quantum bit commitment and strong quantum coin flipping with arbitrarily small bias are impossible in a world subject to superselection rules.

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Additional Information:©2004 The American Physical Society (Received 19 October 2003; published 21 May 2004) We thank Stephen Bartlett, Michael Ben-Or, and Sandu Popescu for discussions. This work has been supported in part by the Department of Energy under Grant No. DEFG03-92-ER40701, by the National Science Foundation under Grant No. EIA-0086038, and by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374.
Subject Keywords:quantum cryptography; information theory; security of data; protocols; quantum computing
Issue or Number:5
Record Number:CaltechAUTHORS:KITpra04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3505
Deposited By: Archive Administrator
Deposited On:09 Jun 2006
Last Modified:08 Nov 2021 19:56

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