Group Theoretical Quantum Tomography

The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.Comment: 13 pages, no figure, Latex2e. Submitted to J.Math.Phy

On right conjugacy closed loops of twice prime order

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl

Quantum memory for images - a quantum hologram

Matter-light quantum interface and quantum memory for light are important ingredients of quantum information protocols, such as quantum networks, distributed quantum computation, etc. In this Letter we present a spatially multimode scheme for quantum memory for light, which we call a quantum hologram. Our approach uses a multi-atom ensemble which has been shown to be efficient for a single spatial mode quantum memory. Due to the multi-atom nature of the ensemble it is capable of storing many spatial modes, a feature critical for the present proposal. A quantum hologram has a higher storage capacity compared to a classical hologram, and is capable of storing quantum features of an image, such as multimode superposition and entangled quantum states, something that a standard hologram is unable to achieve. Due to optical parallelism, the information capacity of the quantum hologram will obviously exceed that of a single-mode scheme.Comment: 5 pages, 3 figure

Two-dimensional Site-Bond Percolation as an Example of Self-Averaging System

The Harris-Aharony criterion for a statistical model predicts, that if a specific heat exponent $\alpha \ge 0$, then this model does not exhibit self-averaging. In two-dimensional percolation model the index $\alpha=-{1/2}$. It means that, in accordance with the Harris-Aharony criterion, the model can exhibit self-averaging properties. We study numerically the relative variances $R_{M}$ and $R_{\chi}$ for the probability $M$ of a site belongin to the "infinite" (maximum) cluster and the mean finite cluster size $\chi$. It was shown, that two-dimensional site-bound percolation on the square lattice, where the bonds play the role of impurity and the sites play the role of the statistical ensemble, over which the averaging is performed, exhibits self-averaging properties.Comment: 15 pages, 5 figure