151 research outputs found
Optimal phase space projection for noise reduction
In this communication we will re-examine the widely studied technique of
phase space projection. By imposing a time domain constraint (TDC) on the
residual noise, we deduce a more general version of the optimal projector,
which includes those appearing in previous literature as subcases but does not
assume the independence between the clean signal and the noise. As an
application, we will apply this technique for noise reduction. Numerical
results show that our algorithm has succeeded in augmenting the signal-to-noise
ratio (SNR) for simulated data from the R\"ossler system and experimental
speech record.Comment: Accepted version for PR
Bayesian estimation of one-parameter qubit gates
We address estimation of one-parameter unitary gates for qubit systems and
seek for optimal probes and measurements. Single- and two-qubit probes are
analyzed in details focusing on precision and stability of the estimation
procedure. Bayesian inference is employed and compared with the ultimate
quantum limits to precision, taking into account the biased nature of Bayes
estimator in the non asymptotic regime. Besides, through the evaluation of the
asymptotic a posteriori distribution for the gate parameter and the comparison
with the results of Monte Carlo simulated experiments, we show that asymptotic
optimality of Bayes estimator is actually achieved after a limited number of
runs. The robustness of the estimation procedure against fluctuations of the
measurement settings is investigated and the use of entanglement to improve the
overall stability of the estimation scheme is also analyzed in some details.Comment: 10 pages, 5 figure
Best network chirplet-chain: Near-optimal coherent detection of unmodeled gravitation wave chirps with a network of detectors
The searches of impulsive gravitational waves (GW) in the data of the
ground-based interferometers focus essentially on two types of waveforms: short
unmodeled bursts and chirps from inspiralling compact binaries. There is room
for other types of searches based on different models. Our objective is to fill
this gap. More specifically, we are interested in GW chirps with an arbitrary
phase/frequency vs. time evolution. These unmodeled GW chirps may be considered
as the generic signature of orbiting/spinning sources. We expect quasi-periodic
nature of the waveform to be preserved independent of the physics which governs
the source motion. Several methods have been introduced to address the
detection of unmodeled chirps using the data of a single detector. Those
include the best chirplet chain (BCC) algorithm introduced by the authors. In
the next years, several detectors will be in operation. The joint coherent
analysis of GW by multiple detectors can improve the sight horizon, the
estimation of the source location and the wave polarization angles. Here, we
extend the BCC search to the multiple detector case. The method amounts to
searching for salient paths in the combined time-frequency representation of
two synthetic streams. The latter are time-series which combine the data from
each detector linearly in such a way that all the GW signatures received are
added constructively. We give a proof of principle for the full sky blind
search in a simplified situation which shows that the joint estimation of the
source sky location and chirp frequency is possible.Comment: 22 pages, revtex4, 6 figure
Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing
Classical and quantum theories of time-symmetric smoothing, which can be used
to optimally estimate waveforms in classical and quantum systems, are derived
using a discrete-time approach, and the similarities between the two theories
are emphasized. Application of the quantum theory to homodyne phase-locked loop
design for phase estimation with narrowband squeezed optical beams is studied.
The relation between the proposed theory and Aharonov et al.'s weak value
theory is also explored.Comment: 13 pages, 5 figures, v2: changed the title to a more descriptive one,
corrected a minor mistake in Sec. IV, accepted by Physical Review
Complete model of a spherical gravitational wave detector with capacitive transducers. Calibration and sensitivity optimization
We report the results of a detailed numerical analysis of a real resonant
spherical gravitational wave antenna operating with six resonant two-mode
capacitive transducers read out by superconducting quantum interference devices
(SQUID) amplifiers. We derive a set of equations to describe the
electro-mechanical dynamics of the detector. The model takes into account the
effect of all the noise sources present in each transducer chain: the thermal
noise associated with the mechanical resonators, the thermal noise from the
superconducting impedance matching transformer, the back-action noise and the
additive current noise of the SQUID amplifier. Asymmetries in the detector
signal-to-noise ratio and bandwidth, coming from considering the transducers
not as point-like objects but as sensor with physically defined geometry and
dimension, are also investigated. We calculate the sensitivity for an
ultracryogenic, 30 ton, 2 meter in diameter, spherical detector with optimal
and non-optimal impedance matching of the electrical read-out scheme to the
mechanical modes. The results of the analysis is useful not only to optimize
existing smaller mass spherical detector like MiniGrail, in Leiden, but also as
a technological guideline for future massive detectors. Furthermore we
calculate the antenna patterns when the sphere operates with one, three and six
resonators. The sky coverage for two detectors based in The Netherlands and
Brasil and operating in coincidence is also estimated. Finally, we describe and
numerically verify a calibration and filtering procedure useful for diagnostic
and detection purposes in analogy with existing resonant bar detectors.Comment: 23 pages, 20 figures, codes of the simulations are available on
request by contacting the autho
Fundamental quantum limits to waveform detection
Ever since the inception of gravitational-wave detectors, limits imposed by
quantum mechanics to the detection of time-varying signals have been a subject
of intense research and debate. Drawing insights from quantum information
theory, quantum detection theory, and quantum measurement theory, here we prove
lower error bounds for waveform detection via a quantum system, settling the
long-standing problem. In the case of optomechanical force detection, we derive
analytic expressions for the bounds in some cases of interest and discuss how
the limits can be approached using quantum control techniques.Comment: v1: first draft, 5 pages; v2: updated and extended, 5 pages +
appendices, 2 figures; v3: 8 pages and 3 figure
Fisher Information for Inverse Problems and Trace Class Operators
This paper provides a mathematical framework for Fisher information analysis
for inverse problems based on Gaussian noise on infinite-dimensional Hilbert
space. The covariance operator for the Gaussian noise is assumed to be trace
class, and the Jacobian of the forward operator Hilbert-Schmidt. We show that
the appropriate space for defining the Fisher information is given by the
Cameron-Martin space. This is mainly because the range space of the covariance
operator always is strictly smaller than the Hilbert space. For the Fisher
information to be well-defined, it is furthermore required that the range space
of the Jacobian is contained in the Cameron-Martin space. In order for this
condition to hold and for the Fisher information to be trace class, a
sufficient condition is formulated based on the singular values of the Jacobian
as well as of the eigenvalues of the covariance operator, together with some
regularity assumptions regarding their relative rate of convergence. An
explicit example is given regarding an electromagnetic inverse source problem
with "external" spherically isotropic noise, as well as "internal" additive
uncorrelated noise.Comment: Submitted to Journal of Mathematical Physic
Statistical Communication Theory
Contains reports on six research projects.National Institutes of Health (Grant MH-04737-02
Multiplet Effects in the Quasiparticle Band Structure of the Anderson Model
In this paper, we examine the mean field electronic structure of the
Anderson lattice model in a slave boson approximation, which should
be useful in understanding the physics of correlated metals with more than one
f electron per site such as uranium-based heavy fermion superconductors. We
find that the multiplet structure of the ion acts to quench the crystal
field splitting in the quasiparticle electronic structure. This is consistent
with experimental observations in such metals as .Comment: 9 pages, revtex, 3 uuencoded postscript figures attached at en
Data analysis of gravitational-wave signals from spinning neutron stars. III. Detection statistics and computational requirements
We develop the analytic and numerical tools for data analysis of the
gravitational-wave signals from spinning neutron stars for ground-based laser
interferometric detectors. We study in detail the statistical properties of the
optimum functional that need to be calculated in order to detect the
gravitational-wave signal from a spinning neutron star and estimate its
parameters. We derive formulae for false alarm and detection probabilities both
for the optimal and the suboptimal filters. We assess the computational
requirements needed to do the signal search. We compare a number of criteria to
build sufficiently accurate templates for our data analysis scheme. We verify
the validity of our concepts and formulae by means of the Monte Carlo
simulations. We present algorithms by which one can estimate the parameters of
the continuous signals accurately.Comment: LaTeX, 45 pages, 13 figures, submitted to Phys. Rev.
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