12,114 research outputs found
Directly Coupled Observers for Quantum Harmonic Oscillators with Discounted Mean Square Cost Functionals and Penalized Back-action
This paper is concerned with quantum harmonic oscillators consisting of a
quantum plant and a directly coupled coherent quantum observer. We employ
discounted quadratic performance criteria in the form of exponentially weighted
time averages of second-order moments of the system variables. A coherent
quantum filtering (CQF) problem is formulated as the minimization of the
discounted mean square of an estimation error, with which the dynamic variables
of the observer approximate those of the plant. The cost functional also
involves a quadratic penalty on the plant-observer coupling matrix in order to
mitigate the back-action of the observer on the covariance dynamics of the
plant. For the discounted mean square optimal CQF problem with penalized
back-action, we establish first-order necessary conditions of optimality in the
form of algebraic matrix equations. By using the Hamiltonian structure of the
Heisenberg dynamics and related Lie-algebraic techniques, we represent this set
of equations in a more explicit form in the case of equally dimensioned plant
and observer.Comment: 11 pages, a brief version to be submitted to the IEEE 2016 Conference
on Norbert Wiener in the 21st Century, 13-15 July, Melbourne, Australi
Methods for Estimating Capacities and Rates of Gaussian Quantum Channels
Optimization methods aimed at estimating the capacities of a general Gaussian
channel are developed. Specifically evaluation of classical capacity as maximum
of the Holevo information is pursued over all possible Gaussian encodings for
the lossy bosonic channel, but extension to other capacities and other Gaussian
channels seems feasible. Solutions for both memoryless and memory channels are
presented. It is first dealt with single use (single-mode) channel where the
capacity dependence from channel's parameters is analyzed providing a full
classification of the possible cases. Then it is dealt with multiple uses
(multi-mode) channel where the capacity dependence from the (multi-mode)
environment state is analyzed when both total environment energy and
environment purity are fixed. This allows a fair comparison among different
environments, thus understanding the role of memory (inter-mode correlations)
and phenomenon like superadditivity of the capacity. The developed methods are
also used for deriving transmission rates with heterodyne and homodyne
measurements at the channel output. Classical capacity and transmission rates
are presented within a unique framework where the rates can be treated as
logarithmic approximations of the capacity.Comment: 39 pages, 30 figures. New results and graphs were added. Errors and
misprints were corrected. To appear in IEEE Trans. Inf. T
Kernel methods in machine learning
We review machine learning methods employing positive definite kernels. These
methods formulate learning and estimation problems in a reproducing kernel
Hilbert space (RKHS) of functions defined on the data domain, expanded in terms
of a kernel. Working in linear spaces of function has the benefit of
facilitating the construction and analysis of learning algorithms while at the
same time allowing large classes of functions. The latter include nonlinear
functions as well as functions defined on nonvectorial data. We cover a wide
range of methods, ranging from binary classifiers to sophisticated methods for
estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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