On communication over an entanglement-assisted quantum channel
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
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)
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Lower bounds in communication complexity based on factorization norms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
ACM SIGACT News
Quantum communication complexity of block-composed functions
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
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Unbounded-error one-way classical and quantum communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A lower bound on entanglement-assisted quantum communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Hi-index | 0.00 |
We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz [22] to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity and nondeterministic quantum communication complexity. We develop several other Fourier based lower bound methods, notably showing that \sqrt {\bar s(f)/\log n}, for the average sensitivity \bar s(f) of a function f, yields a lower bound on the bounded error quantum communication complexity of f(x \wedge y \oplus 2), where x is a Boolean word held by Alice and y, z are Boolean words held by Bob. We then prove the first large lower bounds on the bounded error quantum communication complexity of functions, for which a polynomial quantum speedup is possible. For all the functions we investigate, the only previously applied general lower bound method based on discrepancy yields bounds that are O(log n).