Spatial multipartite entanglement and localization of entanglement

We present a simple model together with its physical implementation which allows one to generate multipartite entanglement between several spatial modes of the electromagnetic field. It is based on parametric down-conversion with N pairs of symmetrically-tilted plane waves serving as a pump. The characteristics of this spatial entanglement are investigated in the cases of zero as well as nonzero phase mismatch. Furthermore, the phenomenon of entanglement localization in just two spatial modes is studied in detail and results in an enhancement of the entanglement by a factor square root of N.Comment: 7 pages, 2 figure

A Christoffel-Darboux formula for multiple orthogonal polynomials

Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux formula for this kernel for general multiple orthogonal polynomials. In addition, we show that the formula can be written in terms of the solution of the Riemann-Hilbert problem for multiple orthogonal polynomials, which will be useful for asymptotic analysis.Comment: 11 pages, no figure

Quantum search by parallel eigenvalue adiabatic passage

We propose a strategy to achieve the Grover search algorithm by adiabatic passage in a very efficient way. An adiabatic process can be characterized by the instantaneous eigenvalues of the pertaining Hamiltonian, some of which form a gap. The key to the efficiency is based on the use of parallel eigenvalues. This allows us to obtain non-adiabatic losses which are exponentially small, independently of the number of items in the database in which the search is performed.Comment: 7 pages, 4 figure

Tripartite entanglement in parametric down-conversion with spatially-structured pump

Most investigations of multipartite entanglement have been concerned with temporal modes of the electromagnetic field, and have neglected its spatial structure. We present a simple model which allows to generate tripartite entanglement between spatial modes by parametric down-conversion with two symmetrically-tilted plane waves serving as a pump. The characteristics of this entanglement are investigated. We also discuss the generalization of our scheme to 2N+1-partite entanglement using 2N symmetrically-tilted plane pump waves. Another interesting feature is the possibility of entanglement localization in just two spatial modes.Comment: 6 pages, 2 figure

Entanglement may enhance the channel capacity in arbitrary dimensions

We consider explicitly two examples of d-dimensional quantum channels with correlated noise and show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of the output mutual information than product states. We obtain a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension, and conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states achieve the channel capacity.Comment: 12 pages, 3 figure

Managing the Real-time Behaviour of a Particle Beam Factory: The CERN Proton Synchrotron Complex and its Timing System Principles

In the CERN 26 Gev Proton Synchrotron (PS) accelerator network, super-cycles are defined as sequences of different kinds of beams produced repetitively [Fig.1]. Each of these beams is characterised by attributes such as particle type, beam energy, its route through the accelerator network, and the final end user. The super-cycle is programmed by means of an editor through which the operational requirements of the physics programme can be described. Each beam in the normal sequence may later be replaced by a set of spare beams automatically depending on software and hardware interlocks and requests presented to the Master Timing Generator (MTG [Glos. 1]). The MTG calculates at run time how each beam is to be manufactured, and sends a telegram [Glos. 3] message to each accelerator, just before each cycle, describing what it should be doing now and during the next cycle. These messages, together with key machine timing events and clocks are encoded onto a timing distribution drop net where they are distributed around the PS complex to VME-standard timing reception TG8 [Glos. 8] modules which generate output pulses and VME bus interrupts for task synchronisation. The TG8 modules are able to use accelerator-related clocks such as the incremental/ decremental magnetic field trains, or the beam revolution and radio frequencies to produce high precision beam synchronous timing. Timing Surveillance Modules (TSM) monitor these timings, which give high precision interval measurements used for the machine tuning, beam diagnostics, and fault detection systems

Properties of Stationary Nonequilibrium States in the Thermostatted Lorentz Gas I: the One Particle System

We study numerically and analytically the properties of the stationary state of a particle moving under the influence of an electric field \bE in a two dimensional periodic Lorentz gas with the energy kept constant by a Gaussian thermostat. Numerically the current appears to be a continuous function of \bE whose derivative varies very irregularly, possibly in a discontinuous manner. We argue for the non differentibility of the current as a function of \bE utilizing a symbolic description of the dynamics based on the discontinuities of the collision map. The decay of correlations and the behavior of the diffusion constant are also investigated

Capacity of a bosonic memory channel with Gauss-Markov noise

We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a "quantum water-filling" solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.Comment: 11 pages, 4 figures, final corrections mad

A note on biorthogonal ensembles

We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It is known that the eigenvalue correlation functions of such ensembles can be written as a determinant of a kernel function. We show that the kernel is itself an average of a single ratio of characteristic polynomials. In the same vein, we prove that the type I multiple polynomials can be expressed as an average of the inverse of a characteristic polynomial. We finally introduce a new biorthogonal matrix ensemble, namely the chiral unitary perturbed by a source term.Comment: 20 page