A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.Comment: 20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references adde

Nouveaux principes de cryptographie utilisant la physique quantique et la théorie du chaos

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LDPC-based Gaussian key reconciliation

International audienceWe propose a new information reconciliation method which allows two parties sharing continuous random variables to agree on a common bit string. We show that existing coded modulation techniques can be adapted for reconciliation and give an explicit code construction based on LDPC codes in the case of Gaussian variables. Simulations show that our method achieves higher efficiency than previously reported results