Complexity Lower Bounds using Linear Algebra
Foundations and Trends® in Theoretical Computer Science
Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
ACM SIGACT News
SIAM Journal on Computing
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
Unbounded-error quantum query complexity
Theoretical Computer Science
On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
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
SIAM Journal on Computing
Multipartite entanglement in XOR games
Quantum Information & Computation
Hadamard tensors and lower bounds on multiparty communication complexity
Computational Complexity
Hi-index | 0.00 |
We prove lower bounds on the 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 [Comput. Complexity, 5 (1995), pp. 205-221] 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 lower bound methods based on the Fourier transform, 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 $f((x \wedge y)\oplus z)$, 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 $O(\log n)$.