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Adiabatic quantum state generation and statistical zero knowledge
The ASG approach to quantum algorithms provides intriguing links between quantum computation and many different areas: the analysis of spectral gaps and groundstates of Hamiltonians in physics, rapidly mixing Markov chains, statistical zero knowledge, and quantum random walks. Expand
Loss-less condensers, unbalanced expanders, and extractors
A clean method is given for overcoming this bottleneck by constructing loss-less condensers, which compress the n-bit input source without losing any min-entropy, using O(\log n) additional random bits. Expand
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
The method of Kovari, Sos, and Turan can be extended to give tight lower bounds for extractors, in terms of both the number of truly random bits needed to extract one additional bit and the unavoidable entropy loss in the system. Expand
Dense quantum coding and quantum finite automata
The technique is applied to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata. Expand
Dense quantum coding and a lower bound for 1-way quantum automata
An exponential lower bound on the size of 1-way quantum finite automata for a family of languages accepted by linear sized deterministic finite automaton is proved. Expand
Quantum bit escrow
Uncondit ionally secure bit commi tmen t and coin flipping are known to be impossible in the classical world. Bit commitment is known to be impossible also in the quan tum world. We introduce aExpand
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
The existence of strongly universal traversal sequences, as well as the solution of the most difficult variant of the deterministic treasure hunt problem, are left as intriguing open problems. Expand
Normal subgroup reconstruction and quantum computation using group representations
It is shown that an immediate generalization of the Abelian case solution to the non-Abelian case does not efficiently solve Graph Isomorphism. Expand
The quantum communication complexity of sampling
An exponential gap is established between quantum and classical sampling complexity, for the set disjointness function, which is the first exponential gap for any task where the classical probabilistic algorithm is allowed to err. Expand
Storing information with extractors
  • A. Ta-Shma
  • Mathematics, Computer Science
  • Inf. Process. Lett.
  • 15 September 2002
A non-explicit optimal construction that is based on the existence of certain good unbalanced expanders, and an explicit construction with about K1+o(1) storing bits, that gets closer to the optimal K log N bound. Expand