dorsal/arxiv
View SchemaSuperselection rules and quantum protocols
| Authors | Alexei Kitaev, Dominic Mayers, John Preskill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310088 |
| URL | https://arxiv.org/abs/quant-ph/0310088 |
| DOI | 10.1103/PhysRevA.69.052326 |
| Journal | Phys.Rev. A69 (2004) 052326 |
Abstract
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 nonabelian 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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"abstract": "We show that superselection rules do not enhance the information-theoretic\nsecurity of quantum cryptographic protocols. Our analysis employs two quite\ndifferent methods. The first method uses the concept of a reference system --\nin a world subject to a superselection rule, unrestricted operations can be\nsimulated by parties who share access to a reference system with suitable\nproperties. By this method, we prove that if an n-party protocol is secure in a\nworld subject to a superselection rule, then the security is maintained even if\nthe superselection rule is relaxed. However, the proof applies only to a\nlimited class of superselection rules, those in which the superselection\nsectors are labeled by unitary irreducible representations of a compact\nsymmetry group. The second method uses the concept of the format of a message\nsent between parties -- by verifying the format, the recipient of a message can\ncheck whether the message could have been sent by a party who performed\ncharge-conserving operations. By this method, we prove that protocols subject\nto general superselection rules (including those pertaining to nonabelian\nanyons in two dimensions) are no more secure than protocols in the unrestricted\nworld. However, the proof applies only to two-party protocols. Our results show\nin particular that, if no assumptions are made about the computational power of\nthe cheater, then secure quantum bit commitment and strong quantum coin\nflipping with arbitrarily small bias are impossible in a world subject to\nsuperselection rules.",
"arxiv_id": "quant-ph/0310088",
"authors": [
"Alexei Kitaev",
"Dominic Mayers",
"John Preskill"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevA.69.052326",
"journal_ref": "Phys.Rev. A69 (2004) 052326",
"title": "Superselection rules and quantum protocols",
"url": "https://arxiv.org/abs/quant-ph/0310088"
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