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Tight bounds on quantum searching
A lower bound on the efficiency of any possible quantum database searching algorithm is provided and it is shown that Grover''s algorithm nearly comes within a factor 2 of being optimal in terms of the number of probes required in the table.
This work generalizes the Grover iteration in the light of a concept called amplitude amplification, and shows that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist.
Private quantum channels
- A. Ambainis, M. Mosca, A. Tapp, R. D. Wolf
- Computer Science, MathematicsProceedings 41st Annual Symposium on Foundations…
- 12 November 2000
It is shown that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sufficient and may be viewed as the quantum analogue of the classical one-time pad encryption scheme.
Authentication of quantum messages
- H. Barnum, C. Crépeau, D. Gottesman, Adam D. Smith, A. Tapp
- Computer Science, PhysicsThe 43rd Annual IEEE Symposium on Foundations of…
- 1 November 2001
A non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s, and a lower bound of 2m key bits for authenticating m qubits is given, which makes the protocol asymptotically optimal.
All Languages in NP Have Very Short Quantum Proofs
- Hugue Blier, A. Tapp
- Mathematics, Computer ScienceThird International Conference on Quantum, Nano…
- 5 September 2007
It is shown that all languages in NP have logarithmic-size quantum proofs which can be verified provided that two unentangled copies are given, and introduces the complexity class QMAlog(2), which is a strong and surprising result.
Quantum cryptanalysis of hash and claw-free functions
A quantum algorithm that finds collisions in arbitrary functions after only O(3√N/τ) expected evaluations of the function, more efficient than the best possible classical algorithm, even allowing probabilism.
Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with what we can and cannot do with quantum information that goes beyond the…
Reversible space equals deterministic space
- Klaus-Jörn Lange, P. McKenzie, A. Tapp
- Computer ScienceProceedings of Computational Complexity. Twelfth…
This paper describes the simulation of an S(n) space-bounded deterministic Turing machine by a reversible Turing machine operating in space S( n) and refutes the conjecture, made by M. Li and P. Vitanyi (1996), that any reversible simulation of a irreversible computation must obey Bennett's reversible pebble game rules.
Cost of Exactly Simulating Quantum Entanglement with Classical Communication
It is shown that, in the case of a single pair of qubits in a Bell state, a constant number of bits of communication is always sufficient — regardless of the number of measurements under consideration.
Quantum Cryptanalysis of Hash and Claw-Free Functions
We give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O(3√N/r) expected evaluations of the function, where N is the cardinality of the domain. Assuming the…