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Using Entanglement in Quantum Multi-Prover Interactive Proofs

Kempe, Julia and Kobayashi, Hirotada and Matsumoto, Keiji and Vidick, Thomas (2009) Using Entanglement in Quantum Multi-Prover Interactive Proofs. Computational Complexity, 18 (2). pp. 273-307. ISSN 1016-3328. doi:10.1007/s00037-009-0275-3.

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The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared among provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show how it can be used to parallelize any multi-prover quantum interactive proof system to a one-round system with perfect completeness, soundness bounded away from one by an inverse-polynomial in the input size, and one extra prover. Alternatively, we can also parallelize to a three-turn system with the same number of provers, where the verifier only broadcasts the outcome of a coin flip. This “public-coin” property is somewhat surprising, since in the classical case public-coin multi-prover interactive proofs are equivalent to single-prover ones.

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Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2009 Birkhäuser Verlag, Basel. Manuscript received 1 September 2008; Published 18 June 2009. We wish to thank Tsuyoshi Ito for suggesting that we include Theorem 5.2 in the paper to characterize the power of one-round public-coin quantum multiprover interactive proofs. Julia Kempe thanks Oded Regev and Amnon TaShma for useful discussions. Julia Kempe was partially supported by the European Commission under the Integrated Project Qubit Applications (QAP) funded by the IST directorate as Contract Number 015848, by an Alon Fellowship of the Israeli Higher Council of Academic Research, by a grant of the Israeli Science Foundation and by a European Research Council (ERC) Starting Grant. Work of Julia Kempe and Thomas Vidick were partly done while at LRI, Université Paris-Sud, Orsay. Hirotada Kobayashi and Keiji Matsumoto were partially supported by the Strategic Information and Communications R&D Promotion Programme No. 031303020 of the Ministry of Internal Affairs and Communications of Japan and the Grant-in-Aid for Scientific Research (B) No. 18300002 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
Funding AgencyGrant Number
European Research Council (ERC)015848
Israeli Higher Council of Academic ResearchUNSPECIFIED
Israel Science FoundationUNSPECIFIED
Ministry of Internal Affairs and Communications (Japan)031303020
Ministry of Education, Culture, Sports, Science and Technology (MEXT)18300002
Subject Keywords:Quantum computing, interactive proof systems, multiprover interactive proof systems, entanglement
Issue or Number:2
Classification Code:MSC: 03D15, 68Q10, 68Q15, 81P68
Record Number:CaltechAUTHORS:20200805-150138118
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Official Citation:Kempe, J., Kobayashi, H., Matsumoto, K. et al. Using Entanglement in Quantum Multi-Prover Interactive Proofs. comput. complex. 18, 273–307 (2009).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104766
Deposited By: Tony Diaz
Deposited On:05 Aug 2020 22:29
Last Modified:16 Nov 2021 18:34

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