187 research outputs found
Stability of uniformly bounded switched systems and Observability
This paper mainly deals with switched linear systems defined by a pair of
Hurwitz matrices that share a common but not strict quadratic Lyapunov
function. Its aim is to give sufficient conditions for such a system to be
GUAS.We show that this property of being GUAS is equivalent to the uniform
observability on of a bilinear system defined on a subspace whose
dimension is in most cases much smaller than the dimension of the switched
system.Some sufficient conditions of uniform asymptotic stability are then
deduced from the equivalence theorem, and illustrated by examples.The results
are partially extended to nonlinear analytic systems
Gaussian Quantum Information
The science of quantum information has arisen over the last two decades
centered on the manipulation of individual quanta of information, known as
quantum bits or qubits. Quantum computers, quantum cryptography and quantum
teleportation are among the most celebrated ideas that have emerged from this
new field. It was realized later on that using continuous-variable quantum
information carriers, instead of qubits, constitutes an extremely powerful
alternative approach to quantum information processing. This review focuses on
continuous-variable quantum information processes that rely on any combination
of Gaussian states, Gaussian operations, and Gaussian measurements.
Interestingly, such a restriction to the Gaussian realm comes with various
benefits, since on the theoretical side, simple analytical tools are available
and, on the experimental side, optical components effecting Gaussian processes
are readily available in the laboratory. Yet, Gaussian quantum information
processing opens the way to a wide variety of tasks and applications, including
quantum communication, quantum cryptography, quantum computation, quantum
teleportation, and quantum state and channel discrimination. This review
reports on the state of the art in this field, ranging from the basic
theoretical tools and landmark experimental realizations to the most recent
successful developments.Comment: 51 pages, 7 figures, submitted to Reviews of Modern Physic
Quantum theory without Hilbert spaces
Quantum theory does not only predict probabilities, but also relative phases
for any experiment, that involves measurements of an ensemble of systems at
different moments of time. We argue, that any operational formulation of
quantum theory needs an algebra of observables and an object that incorporates
the information about relative phases and probabilities. The latter is the
(de)coherence functional, introduced by the consistent histories approach to
quantum theory. The acceptance of relative phases as a primitive ingredient of
any quantum theory, liberates us from the need to use a Hilbert space and
non-commutative observables. It is shown, that quantum phenomena are adequately
described by a theory of relative phases and non-additive probabilities on the
classical phase space. The only difference lies on the type of observables that
correspond to sharp measurements. This class of theories does not suffer from
the consequences of Bell's theorem (it is not a theory of Kolmogorov
probabilities) and Kochen- Specker's theorem (it has distributive "logic"). We
discuss its predictability properties, the meaning of the classical limit and
attempt to see if it can be experimentally distinguished from standard quantum
theory. Our construction is operational and statistical, in the spirit of
Kopenhagen, but makes plausible the existence of a realist, geometric theory
for individual quantum systems.Comment: 32 pages, Latex, 4 figures. Small changes in the revised version,
comments and references added; essentially the version to appear in Found.
Phy
Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis
Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015von Philipp Rumschinsk
Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols
While feedback control has many applications in quantum systems, finding
optimal control protocols for this task is generally challenging. So-called
"verification theorems" and "viscosity solutions" provide two useful tools for
this purpose: together they give a simple method to check whether any given
protocol is optimal, and provide a numerical method for finding optimal
protocols. While treatments of verification theorems usually use sophisticated
mathematical language, this is not necessary. In this article we give a simple
introduction to feedback control in quantum systems, and then describe
verification theorems and viscosity solutions in simple language. We also
illustrate their use with a concrete example of current interest.Comment: 12 pages, revtex
Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods
Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided
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