19,293 research outputs found
Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model
with data in a sequential fashion. Despite its widespread use, there has been
little analysis of its theoretical properties. Many of the algorithmic
innovations associated with the filter, which are required to make a useable
algorithm in practice, are derived in an ad hoc fashion. The aim of this paper
is to initiate the development of a systematic analysis of the EnKF, in
particular to do so in the small ensemble size limit. The perspective is to
view the method as a state estimator, and not as an algorithm which
approximates the true filtering distribution. The perturbed observation version
of the algorithm is studied, without and with variance inflation. Without
variance inflation well-posedness of the filter is established; with variance
inflation accuracy of the filter, with resepct to the true signal underlying
the data, is established. The algorithm is considered in discrete time, and
also for a continuous time limit arising when observations are frequent and
subject to large noise. The underlying dynamical model, and assumptions about
it, is sufficiently general to include the Lorenz '63 and '96 models, together
with the incompressible Navier-Stokes equation on a two-dimensional torus. The
analysis is limited to the case of complete observation of the signal with
additive white noise. Numerical results are presented for the Navier-Stokes
equation on a two-dimensional torus for both complete and partial observations
of the signal with additive white noise
Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics
We study transport through an electronic Mach-Zehnder interferometer recently
devised at the Weizmann Institute. We show that this device can be used to
probe statistics of quasiparticles in the fractional quantum Hall regime. We
calculate the tunneling current through the interferometer as the function of
the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its
flux-dependent component is strongly sensitive to the statistics of tunneling
quasiparticles. More specifically, the flux-dependent and flux-independent
contributions to the current are related by a power law, the exponent being a
function of the quasiparticle statistics.Comment: 22 pages; 8 figure
Device-independent bounds for Hardy's experiment
In this Letter we compute an analogue of Tsirelson's bound for Hardy's test
of nonlocality, that is, the maximum violation of locality constraints allowed
by the quantum formalism, irrespective of the dimension of the system. The
value is found to be the same as the one achievable already with two-qubit
systems, and we show that only a very specific class of states can lead to such
maximal value, thus highlighting Hardy's test as a device-independent self-test
protocol for such states. By considering realistic constraints in Hardy's test,
we also compute device-independent upper bounds on this violation and show that
these bounds are saturated by two-qubit systems, thus showing that there is no
advantage in using higher-dimensional systems in experimental implementations
of such test.Comment: 4 pages, 2 figure
Analysis and interpretation of high transverse entanglement in optical parametric down conversion
Quantum entanglement associated with transverse wave vectors of down
conversion photons is investigated based on the Schmidt decomposition method.
We show that transverse entanglement involves two variables: orbital angular
momentum and transverse frequency. We show that in the monochromatic limit high
values of entanglement are closely controlled by a single parameter resulting
from the competition between (transverse) momentum conservation and
longitudinal phase matching. We examine the features of the Schmidt eigenmodes,
and indicate how entanglement can be enhanced by suitable mode selection
methods.Comment: 4 pages, 4 figure
Wave attenuation and dispersion due to floating ice covers
Experiments investigating the attenuation and dispersion of surface waves in
a variety of ice covers are performed using a refrigerated wave flume. The ice
conditions tested in the experiments cover naturally occurring combinations of
continuous, fragmented, pancake and grease ice. Attenuation rates are shown to
be a function of ice thickness, wave frequency, and the general rigidity of the
ice cover. Dispersion changes were minor except for large wavelength increases
when continuous covers were tested. Results are verified and compared with
existing literature to show the extended range of investigation in terms of
incident wave frequency and ice conditions
Generating entangled photon pairs from a cavity-QED system
We propose a scheme for the controlled generation of Einstein-Podosky-Rosen
(EPR) entangled photon pairs from an atom coupled to a high Q optical cavity,
extending the prototype system as a source for deterministic single photons. A
thorough theoretical analysis confirms the promising operating conditions of
our scheme as afforded by currently available experimental setups. Our result
demonstrates the cavity QED system as an efficient and effective source for
entangled photon pairs, and shines new light on its important role in quantum
information science.Comment: It has recently come to our attention that the experiment by T. Wilk,
S. C. Webster, A. Kuhn and G. Rempe, published in Science 317, 488 (2007),
exactly realizes what we proposed in this article, which is published in Phy.
Rev. A 040302(R) (2005
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