Multilinear formulas and skepticism of quantum computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Exponential separation of quantum and classical one-way communication complexity
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Tensor norms and the classical communication complexity of nonlocal quantum measurement
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Limits on the ability of quantum states to convey classical messages
Journal of the ACM (JACM)
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Quantum one-way communication can be exponentially stronger than classical communication
Proceedings of the forty-third annual ACM symposium on Theory of computing
On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
Quantum and classical message protect identification via quantum channels
Quantum Information & Computation
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
The Complexity of Distributions
SIAM Journal on Computing
SIAM Journal on Computing
A lower bound on entanglement-assisted quantum communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function $f: X \times Y \rightarrow \{0,1\}$ and a probability distribution ${\cal D}$ over $X \times Y$, we define the sampling complexity of $(f, {\cal D})$ as the minimum number of bits that Alice and Bob must communicate for Alice to pick $x \in X$ and Bob to pick $y \in Y$ as well as a value $z$ such that the resulting distribution of $(x,y,z)$ is close to the distribution $({\cal D}, f({\cal D}))$.In this paper we initiate the study of sampling complexity, in both the classical and quantum models. We give several variants of a definition. We completely characterize some of these variants and give upper and lower bounds on others. In particular, this allows us to establish an exponential gap between quantum and classical sampling complexity for the set-disjointness function.