Kolmogorov Complexity and Combinatorial Methods in Communication Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Theoretical Computer Science
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
Composition theorems in communication complexity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Kolmogorov complexity and combinatorial methods in communication complexity
Theoretical Computer Science
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
Non-local box complexity and secure function evaluation
Quantum Information & Computation
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The communication complexity of non-signaling distributions
Quantum Information & Computation
SIAM Journal on Computing
Classical and quantum partition bound and detector inefficiency
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The approximate rank of a matrix and its algorithmic applications: approximate rank
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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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. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009