Quantum zero-error algorithms cannot be composed
Information Processing Letters
Exponential separation of quantum and classical online space complexity
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Quantum certificate complexity
Journal of Computer and System Sciences
Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Unbounded-error quantum query complexity
Theoretical Computer Science
Quantum weakly nondeterministic communication complexity
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Tensor rank and strong quantum nondeterminism in multiparty communication
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Quantum weakly nondeterministic communication complexity
Theoretical Computer Science
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We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f(x)=1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a Boolean function is equal to its "nondeterministic polynomial" degree. We also prove a quantum-vs.-classical gap of 1 vs. n for nondeterministic query complexity for a total function. In the setting of communication complexity, we show that the nondeterministic quantum complexity of a two-party function is equal to the logarithm of the rank of a nondeterministic version of the communication matrix. This implies that the quantum communication complexities of the equality and disjointness functions are n+1 if we do not allow any error probability. We also exhibit a total function in which the nondeterministic quantum communication complexity is exponentially smaller than its classical counterpart.