Information-theoretic principle entails orthomodularity of a lattice

Quantum logical axiomatic systems for quantum theory usually include a postulate that a lattice under consideration is orthomodular. We propose a derivation of orthomodularity from an information-theoretic axiom. This provides conceptual clarity and removes a long-standing puzzle about the meaning of orthomodularity.Comment: Version prior to published, with slight modification

Polar codes and polar lattices for the Heegard-Berger problem

Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for doublysymmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting a quantization polar lattice and a capacity-achieving polar lattice for the additive white Gaussian noise channel

Confronting Instanton Perturbation Theory with QCD Lattice Results

We exploit a recent lattice investigation (UKQCD) on the topological structure of the (quenched) QCD vacuum, in order to gain information on crucial building blocks of instanton perturbation theory. A central motivation is to further constrain our previous predictions of instanton-induced hard scattering processes. First, we address the generic problem of extracting quantitative information from cooled lattice data. We find a new scaling variable, interpreted as a "cooling radius", which allows to combine lattice data for a whole range of lattice spacings and cooling sweeps. This variable strongly helps to extract information on the uncooled distributions of interest. After performing the continuum extrapolation of the instanton size and instanton-anti-instanton distance distributions, we find striking agreement with the theoretical predictions from instanton-perturbation theory, for instanton sizes below 0.5 fm and distances above 0.5 fm, respectively. These results imply first direct support for the validity of the known valley interaction between instantons and anti-instantons.Comment: 14 pages, 6 figures, submitted to Physics Letters