Quantum entanglement and the communication complexity of the inner product function

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The authors 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. They prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. The proofs employ a novel kind of quantum reduction from multibit communication problems 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. They also give a specific example of ... continued below

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14 p.

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Cleve, R.; Dam, W. van; Nielsen, M. & Tapp, A. August 1, 1998.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 32 times , with 6 in the last month . More information about this article can be viewed below.

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  • Cleve, R. Univ. of Calgary, Alberta (Canada)
  • Dam, W. van Univ. of Oxford (United Kingdom)
  • Nielsen, M. Univ. of New Mexico, Albuquerque, NM (United States)
  • Tapp, A. Univ. de Montreal, Quebec (Canada)

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Description

The authors 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. They prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. The proofs employ a novel kind of quantum reduction from multibit communication problems 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. They also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.

Physical Description

14 p.

Notes

OSTI as DE98003710

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  • 1. NASA international conference on quantum computing and quantum communications, Palm Springs, CA (United States), 15-20 Feb 1998

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  • Other: DE98003710
  • Report No.: LA-UR--98-725
  • Report No.: CONF-980245--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 661703
  • Archival Resource Key: ark:/67531/metadc706249

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Office of Scientific & Technical Information Technical Reports

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  • August 1, 1998

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • Oct. 3, 2017, 12:53 p.m.

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Cleve, R.; Dam, W. van; Nielsen, M. & Tapp, A. Quantum entanglement and the communication complexity of the inner product function, article, August 1, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc706249/: accessed November 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.