Lower bounds in communication complexity based on factorization norms

Nati Linial, Adi Shraibman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


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 to several 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
Pages (from-to)368-394
Number of pages27
JournalRandom Structures and Algorithms
Issue number3
StatePublished - May 2009


  • Banach Spaces
  • Communication complexity
  • Factorization norms
  • Lower bounds


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