Elements of information theory
Elements of information theory
Direct product results and the GCD problem, in old and new communication models
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Communication complexity
SIAM Journal on Computing
Dense quantum coding and a lower bound for 1-way quantum automata
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On randomized one-round communication complexity
Computational Complexity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Limitations of Quantum Advice and One-Way Communication
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Towards proving strong direct product theorems
Computational Complexity
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
An Optimal Randomised Cell Probe Lower Bound for Approximate Nearest Neighbour Searching
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Higher Lower Bounds for Near-Neighbor and Further Rich Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Perfect Parallel Repetition Theorem for Quantum XOR Proof Systems
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Communication Complexity under Product and Nonproduct Distributions
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
On the role of shared entanglement
Quantum Information & Computation
Quantum and classical communication-space tradeoffs from rectangle bounds
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Classical interaction cannot replace a quantum message
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
New bounds on classical and quantum one-way communication complexity
Theoretical Computer Science
Kolmogorov Complexity and Combinatorial Methods in Communication Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
A property of quantum relative entropy with an application to privacy in quantum communication
Journal of the ACM (JACM)
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
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
On the power of lower bound methods for one-way quantum communication complexity
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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
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
Communication lower bounds using directional derivatives
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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A basic question in complexity theory is whether the computational resources required for solving k independent instances of the same problem scale as k times the resources required for one instance. We investigate this question in various models of classical communication complexity. We introduce a new measure, the subdistribution bound , which is a relaxation of the well-studied rectangle or corruption bound in communication complexity. We nonetheless show that for the communication complexity of Boolean functions with constant error, the subdistribution bound is the same as the latter measure, up to a constant factor. We prove that the one-way version of this bound tightly captures the one-way public-coin randomized communication complexity of any relation, and the two-way version bounds the two-way public-coin randomized communication complexity from below. More importantly, we show that the bound satisfies the strong direct product property under product distributions for both one- and two-way protocols, and the weak direct product property under arbitrary distributions for two-way protocols. These results subsume and strengthen, in a unified manner, several recent results on the direct product question. The simplicity and broad applicability of our technique is perhaps an indication of its potential to solve yet more challenging questions regarding the direct product problem.