520 research outputs found
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
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