Multiparty protocols and logspace-hard pseudorandom sequences
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Private vs. common random bits in communication complexity
Information Processing Letters
Fractional Covers and Communication Complexity
SIAM Journal on Discrete Mathematics
Public vs. private coin flips in one round communication games (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On Quantum Versions of the Yao Principle
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Quantum Moment Problem and Bounds on Entangled Multi-prover Games
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Exponential Separation of Quantum and Classical One-Way Communication Complexity
SIAM Journal on Computing
Lower bounds in communication complexity based on factorization norms
Random Structures & Algorithms
SIAM Journal on Computing
The Partition Bound for Classical Communication Complexity and Query Complexity
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Quantum one-way communication can be exponentially stronger than classical communication
Proceedings of the forty-third annual ACM symposium on Theory of computing
Near-Optimal and Explicit Bell Inequality Violations
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
The communication complexity of non-signaling distributions
Quantum Information & Computation
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We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell experiments, where two players share a predefined entangled state but are not allowed to communicate. Each is given a measurement as input, which they perform on their share of the system. The outcomes of the measurements should follow a distribution predicted by quantum mechanics; however, in practice, the detectors may fail to produce an output in some of the runs. The efficiency of the experiment is the probability that neither of the detectors fails. When the players share a quantum state, this leads to a new bound on quantum communication complexity (eff*) that subsumes the factorization norm. When players share randomness instead of a quantum state, the efficiency bound (eff), coincides with the partition bound of Jain and Klauck. This is one of the strongest lower bounds known for randomized communication complexity, which subsumes all the known combinatorial and algebraic methods including the rectangle (corruption) bound, the factorization norm, and discrepancy. The lower bound is formulated as a convex optimization problem. In practice, the dual form is more feasible to use, and we show that it amounts to constructing an explicit Bell inequality (for eff) or Tsirelson inequality (for eff*). For one-way communication, we show that the quantum one-way partition bound is tight for classical communication with shared entanglement up to arbitrarily small error.