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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 the algorithm. This allows us to determine the number of iterations necessary to achieve almost certainty of nding the answer. Furthermore, we analyse the behaviour of(More)
An unknown quantum state ji can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EPR correlations. To do so the sender, \Alice," and the receiver, \Bob," must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum(More)
Consider a Boolean function χ : X → {0, 1} that partitions set X between its good and bad elements, where x is good if χ(x) = 1 and bad otherwise. Consider also a quantum algorithm A such that A|0 = x∈X αx|x is a quantum superposition of the elements of X, and let a denote the probability that a good element is produced if A|0 is measured. If we repeat the(More)
Recently a great deal of attention has been focused on quantum computation following a sequence of results [Bernstein and Vazirani, in Proc. suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time,(More)
~ This paper provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard and Robert [l] for a special scenario. The results have applications to unconditionally-secure secret-key agreement protocols , quantum cryptography and to a non-asymptotic and constructive treatment of the secrecy capacity of(More)
Protocols are given for allowing a " prover " to convince a " verifier " that the prover knows some verifiable secret information, without allowing the verifier to learn anything about the secret. The secret can be probabilistically or deterministically verifiable, and only one of the prover or the verifier need have constrained resources. This paper(More)
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's problem can be solved in this way, whereas previous algorithms required quantum polynomial time in the expected sense(More)