Motion Caused by Magnetic Field in Lobachevsky Space

We study motion of a relativistic particle in the 3-dimensional Lobachevsky space in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in the Euclidean space. Three integrals of motion are found and equations of motion are solved exactly in the special cylindrical coordinates. Motion on surface of the cylinder of constant radius is considered in detail.Comment: 4 page

Study of Stability of a Charged Topological Soliton in the System of Two Interacting Scalar Fields

An analytical-numerical analysis of the singular self-adjoint spectral problem for a system of three linear ordinary second-order differential equations defined on the entire real exis is presented. This problem comes to existence in the nonlinear field theory. The dependence of the differential equations on the spectral parameter is nonlinear, which results in a quadratic operator Hermitian pencil.Comment: 22 pages, 2 figure

Synthesis of the Einstein-Podolsky-Rosen entanglement in a sequence of two single-mode squeezers

Synthesis of the Einstein-Podolsky-Rosen entangled state --- the primary entangled resource in continuous-variable quantum-optical information processing --- is a technological challenge of great importance. Here we propose and implement a new scheme of generating this state. Two nonlinear optical crystals, positioned back-to-back in the waist of a pump beam, function as single-pass degenerate optical parametric amplifiers and produce single-mode squeezed vacuum states in orthogonal polarization modes, but in the same spatiotemporal mode. A subsequent pair of waveplates acts as a beam splitter, entangling the two polarization modes to generate the Einstein-Podolsky-Rosen state. This technique takes advantage of the strong nonlinearity associated with type-I phase-matching configuration while at the same time eliminating the need for actively stabilizing the optical phase between the two squeezers, which typically arises if these squeezers are spatially separated. We demonstrate our method in an experiment, preparing a 1.4 dB two-mode squeezed state and characterizing it via two-mode homodyne tomography.Comment: 4 pages, 3 figure

Post-processing procedure for industrial quantum key distribution systems

We present algorithmic solutions aimed on post-processing for industrial quantum key distribution systems with hardware sifting. The main steps of the procedure are error correction, parameter estimation, and privacy amplification. Authentication of a classical public communication channel is also considered.Comment: 5 pages; presented at the 3rd International School and Conference "Saint-Petersburg OPEN 2016" (Saint-Petersburg, March 28-30, 2016