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Quantum Entanglement and the Communication Complexity of the Inner Product Function

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Quantum Computing and Quantum Communications (QCQC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1509))

Abstract

We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. Our proofs employ a novel kind of “quantum„ reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo’s theorem. We also give a speciffic example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.

Research initiated while visiting the Université de Montréal and supported in part by Canada’s NSERC.

Research supported in part by Canada’s NSERC.

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Author information

Authors and Affiliations

  1. University of Calgary Department of Computer Science, University of Calgary, Calgary, Alberta, Canada, T2N 1N4

    Richard Cleve

  2. University of Oxford and CWI, Amsterdam Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK

    Wim van Dam

  3. Los Alamos National Laboratory and University of New Mexico, Los Alamos National Laboratory, T-6 Theoretical Astrophysics, USA

    Michael Nielsen

  4. Département IRO, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, Canada, H3C 3J7

    Alain Tapp

Authors
  1. Richard Cleve
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  2. Wim van Dam
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  3. Michael Nielsen
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  4. Alain Tapp
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Editor information

Editors and Affiliations

  1. Jet Propulsion Laboratory, California Institute of Technology Quantum Algorithms and Technologies Group Information and Computing Technologies Research Section, Mail Stop 126-347, Pasadena, CA, 91109-8099, USA

    Colin P. Williams

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© 1999 Springer-Verlag Berlin Heidelberg

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Cleve, R., van Dam, W., Nielsen, M., Tapp, A. (1999). Quantum Entanglement and the Communication Complexity of the Inner Product Function. In: Williams, C.P. (eds) Quantum Computing and Quantum Communications. QCQC 1998. Lecture Notes in Computer Science, vol 1509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49208-9_4

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  • DOI: https://doi.org/10.1007/3-540-49208-9_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65514-5

  • Online ISBN: 978-3-540-49208-5

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