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We provide a tight analysis of Grover's algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of theâ€¦ (More)

Consider a Boolean function Ï‡ : X â†’ {0, 1} that partitions set X between its good and bad elements, where x is good if Ï‡(x) = 1 and bad otherwise. Consider also a quantum algorithm A such that A|0ã€‰ =â€¦ (More)

- Andris Ambainis, Michele Mosca, Alain Tapp, Ronald de Wolf
- FOCS
- 2000

We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. In particular we showâ€¦ (More)

- Klaus-JÃ¶rn Lange, Pierre McKenzie, Alain Tapp
- IEEE Conference on Computational Complexity
- 1997

This paper describes the simulation of an S(n) space-bounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by Bennett in 1989â€¦ (More)

Authentication is a well-studied area of classical cryptography: a sender A and a receiver B sharing a classical private key want to exchange a classical message with the guarantee that the messageâ€¦ (More)

- Richard Cleve, Wim van Dam, Michael Nielsen, Alain Tapp
- QCQC
- 1998

We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantumâ€¦ (More)

- Gilles Brassard, Peter HÃ¸yer, Alain Tapp
- ICALP
- 1998

We study some extensions of Groverâ€™s quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadraticâ€¦ (More)

We investigate the amount of communication that must augment classical local hidden variable models in order to simulate the behaviour of entangled quantum systems. We consider the scenario where aâ€¦ (More)

- Gilles Brassard, Peter HÃ¸yer, Alain Tapp
- Encyclopedia of Algorithms
- 2008

In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O( 3 âˆš N/r ) expected evaluations of the function. Assuming the function is given by a blackâ€¦ (More)

- Gilles Brassard, Peter HÃ¸yer, Alain Tapp
- LATIN
- 1997

In this note, we give a quantum algorithm that finds collisions in arbitrary τ-to-one functions after only O(3√N/τ) expected evaluations of the function. Assuming the function is givenâ€¦ (More)