Lower bounds in communication complexity based on factorization norms

Nati Linial*, Adi Shraibman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

29 Scopus citations

Abstract

We introduce a new method to derive lower bounds on randomized and quantum communication complexity. Our method is based on factorization norms, a notion from Banach Space theory. This approach gives us access toseveral powerful tools from this area such as normed spaces duality and Grothendiek's inequality. This extends the arsenal of methods for deriving lower bounds in communication complexity. As we show,our method subsumes most of the previously known general approaches to lower bounds on communication complexity. Moreover, we extend all (but one) of these lower bounds to the realm of quantum communication complexity with entanglement. Our results also shed some light on the question how much communication can be saved by using entanglement.It is known that entanglement can save one of every two qubits, and examples for which this is tight are also known. It follows from our results that this bound on the saving in communication is tight almost always.

Original languageAmerican English
Title of host publicationSTOC'07
Subtitle of host publicationProceedings of the 39th Annual ACM Symposium on Theory of Computing
Pages699-708
Number of pages10
DOIs
StatePublished - 2007
EventSTOC'07: 39th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States
Duration: 11 Jun 200713 Jun 2007

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

ConferenceSTOC'07: 39th Annual ACM Symposium on Theory of Computing
Country/TerritoryUnited States
CitySan Diego, CA
Period11/06/0713/06/07

Keywords

  • Communication complexity
  • Discrepancy
  • Factorization norms
  • Fourier analysis

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