A numerical investigation of motion near the lagrangian points of the sun-saturn system

The motion of test particles near the Lagrangian triangular points of the Sun-Saturn system are studied by the numerical integrations of the equations of motion. The three-dimensional, elliptic, restricted seven-body problem is considered (for the bodies are the Sun, five outer planets, and a small body). It is shown that tadpole orbits points break down in close neighborhood of the Lagrangian on a timescale of 100 kyr. The regions of stable libration oscillations at t ∼ 100 kyr have an annular shape. Motion in tadpole orbits persists over at least 100 kyr at ΔH - 20° and Δr ≈ ±0.1-0.2 AU, where Δr is the heliocentric-distance difference between the particle and the Lagrangian point, ΔH is the angle between the direction to the libration point and the direction to the particle at the initial moment. © 1999 MAHK "Hayka/Interperiodica"

Heralded gate search with genetic algorithms for quantum computation

In this paper we present genetic algorithms based search technique for the linear optics schemes, performing two-qubit quantum gates. We successfully applied this technique for finding heralded two-qubit gates and obtained the new schemes with performance parameters equal to the best currently known. The new simple metrics is introduced which enables comparison of schemes with different heralding mechanisms. The scheme performance degradation is discussed for the cases when detectors in the heralding part of the scheme are not photon-number-resolving. We propose a procedure for overcoming this drawback which allows us to restore the reliable heralding signal even with not-photon-number-resolving detectors

Quantum parallel dense coding of optical images

We propose quantum dense coding protocol for optical images. This protocol extends the earlier proposed dense coding scheme for continuous variables [S.L.Braunstein and H.J.Kimble, Phys.Rev.A 61, 042302 (2000)] to an essentially multimode in space and time optical quantum communication channel. This new scheme allows, in particular, for parallel dense coding of non-stationary optical images. Similar to some other quantum dense coding protocols, our scheme exploits the possibility of sending a classical message through only one of the two entangled spatially-multimode beams, using the other one as a reference system. We evaluate the Shannon mutual information for our protocol and find that it is superior to the standard quantum limit. Finally, we show how to optimize the performance of our scheme as a function of the spatio-temporal parameters of the multimode entangled light and of the input images.Comment: 15 pages, 4 figures, RevTeX4. Submitted to the Special Issue on Quantum Imaging in Journal of Modern Optic

Error of an arbitrary single-mode Gaussian transformation on a weighted cluster state using a cubic phase gate

In this paper, we propose two strategies for decreasing the error of arbitrary single-mode Gaussian transformations implemented using one-way quantum computation on a four-node linear cluster state. We show that it is possible to minimize the error of the arbitrary single-mode Gaussian transformation by a proper choice of the weight coefficients of the cluster state. We modify the computation scheme by adding a non-Gaussian state obtained using a cubic phase gate as one of the nodes of the cluster. This further decreases the computation error. We evaluate the efficiencies of the proposed optimization schemes comparing the probabilities of the error correction of the quantum computations with and without optimizations. We have shown that for some transformations, the error probability can be reduced by up to 900 times.Comment: 14 pages, 8 figure

Feynman Diagrams and Differential Equations

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D=4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.Comment: invited review article from Int. J. Mod. Phys.