3,302 research outputs found
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
Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann
spaces is studied in the presence of an external magnetic field which is
analogous to a constant uniform magnetic field in Euclidean space. In both
cases three integrals of motions are constructed and equations of motion are
solved exactly in the special cylindrical coordinates on the base of the method
of separation of variables. In Lobachevsky space there exist trajectories of
two types, finite and infinite in radial variable, in Riemann space all motions
are finite and periodical. The invariance of the uniform magnetic field in
tensor description and gauge invariance of corresponding 4-potential
description is demonstrated explicitly. The role of the symmetry is clarified
in classification of all possible solutions, based on the geometric symmetry
group, SO(3,1) and SO(4) respectively
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
Undoing the effect of loss on quantum entanglement
Entanglement distillation is a process via which the strength and purity of
quantum entanglement can be increased probabilistically. It is a key step in
many quantum communication and computation protocols. In particular,
entanglement distillation is a necessary component of the quantum repeater, a
device which counters the degradation of entanglement that inevitably occurs
due to losses in a communication line. Here we report an experiment on
distilling the Einstein-Podolsky-Rosen (EPR) state of light, the workhorse of
continuous-variable entanglement, using the technique of noiseless
amplification. In contrast to previous implementations, the entanglement
enhancement factor achievable by our technique is not fundamentally limited and
permits recovering an EPR state with a macroscopic level of entanglement no
matter how low the initial entanglement or how high the loss may be. In
particular, we recover the original level of entanglement after one of the EPR
modes has passed through a channel with a loss factor of 20. The level of
entanglement in our distilled state is higher than that achievable by direct
transmission of any state through a similar loss channel. This is a key
bench-marking step towards the realization of a practical continuous-variable
quantum repeater and other CV quantum protocols.Comment: 8 pages, 5 figure
- …