Strengths and weaknesses of quantum fingerprinting

Dmitry Gavinsky, Julia Kempe, Ronald De Wolf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the power of quantum fingerprints in the simultaneous message passing (SMP) setting of communication complexity. Yao recently showed how to simulate, with exponential overhead, classical shared-randomness SMP protocols by means of quantum SMP protocols without shared randomness (Q -protocols). Our first result is to extend Yao's simulation to the strongest possible model: every many-round quantum protocol with unlimited shared entanglement can be simulated, with exponential overhead, by Q| -protocols. We apply our technique to obtain an efficient Q -protocol for a function which cannot be efficiently solved through more restricted simulations. Second, we tightly characterize the power of the quantum fingerprinting technique by making a connection to arrangements of homogeneous halfspaces with maximal margin. These arrangements have been well studied in computational learning theory, and we use some strong results obtained in this area to exhibit weaknesses of quantum fingerprinting. In particular, this implies that for almost all functions, quantum fingerprinting protocols are exponentially worse than classical deterministic SMP protocols.

Original languageEnglish (US)
Title of host publicationProceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006
Pages288-295
Number of pages8
Volume2006
DOIs
StatePublished - Dec 1 2006
Event21st Annual IEEE Conference on Computational Complexity, CCC 2006 - Prague, Czech Republic
Duration: Jul 16 2006Jul 20 2006

Other

Other21st Annual IEEE Conference on Computational Complexity, CCC 2006
CountryCzech Republic
CityPrague
Period7/16/067/20/06

Fingerprint

Fingerprinting
Message passing
Message Passing
Randomness
Arrangement
Computational Learning Theory
Communication Complexity
Communication
Fingerprint
Entanglement
Half-space
Margin
Simulation
Imply

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics

Cite this

Gavinsky, D., Kempe, J., & De Wolf, R. (2006). Strengths and weaknesses of quantum fingerprinting. In Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006 (Vol. 2006, pp. 288-295). [1663745] https://doi.org/10.1109/CCC.2006.39

Strengths and weaknesses of quantum fingerprinting. / Gavinsky, Dmitry; Kempe, Julia; De Wolf, Ronald.

Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. Vol. 2006 2006. p. 288-295 1663745.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Gavinsky, D, Kempe, J & De Wolf, R 2006, Strengths and weaknesses of quantum fingerprinting. in Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. vol. 2006, 1663745, pp. 288-295, 21st Annual IEEE Conference on Computational Complexity, CCC 2006, Prague, Czech Republic, 7/16/06. https://doi.org/10.1109/CCC.2006.39
Gavinsky D, Kempe J, De Wolf R. Strengths and weaknesses of quantum fingerprinting. In Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. Vol. 2006. 2006. p. 288-295. 1663745 https://doi.org/10.1109/CCC.2006.39
Gavinsky, Dmitry ; Kempe, Julia ; De Wolf, Ronald. / Strengths and weaknesses of quantum fingerprinting. Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. Vol. 2006 2006. pp. 288-295
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