481 research outputs found
Symmetry Reduction of Quasi-Free States
Given a group-invariant quasi-free state on the algebra of canonical
commutation relations (CCR), we show how group averaging techniques can be used
to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the
group is compact this method of symmetry reduction leads to standard results
which can be obtained using other methods. When the group is non-compact the
group averaging prescription relies upon technically favorable conditions which
we delineate. As an example, we consider symmetry reduction of the usual vacuum
state for a Klein-Gordon field on Minkowski spacetime by a non-compact subgroup
of the Poincar\'e group consisting of a 1-parameter family of boosts, a
1-parameter family of spatial translations and a set of discrete translations.
We show that the symmetry reduced CCR algebra and vacuum state correspond to
that used by each of Berger, Husain, and Pierri for the polarized Gowdy quantum gravity model.Comment: 18 page
Point Estimation of States of Finite Quantum Systems
The estimation of the density matrix of a -level quantum system is studied
when the parametrization is given by the real and imaginary part of the entries
and they are estimated by independent measurements. It is established that the
properties of the estimation procedure depend very much on the invertibility of
the true state. In particular, in case of a pure state the estimation is less
efficient. Moreover, several estimation schemes are compared for the unknown
state of a qubit when one copy is measured at a time. It is shown that the
average mean quadratic error matrix is the smallest if the applied observables
are complementary. The results are illustrated by computer simulations.Comment: 16 pages, 5 figure
The missing link? Design for all elements in ICT education fostering e-inclusion.
Accessible Information and Communication Technology (ICT) systems and applications are able to offer an important opportunity for social, political and economic engagement.
Additionally, the established principles and practices of Design for All could help to minimise the risk of exclusion of citizens from the information society such as older adults, disabled people, people with low literacy or those not using their first language But what if the future providers of ICT solutions and applications lack the knowledge of Design for All principles and practices, and the skills to apply that knowledge to support innovation and advancement
Design for all as focus in European ICT teaching and training activities.
Both in the EU and UK the goal of digital inclusion demands a broad understanding of the factors that contribute to the risk of exclusion, such as a result of age, disability, low literacy, geography and ethnicity. The overall methodologies and principles of Design for All are well established and address many of the challenges of design for user diversity including older and disabled people. However, these are not yet an established part of the curriculum in mainstream Computing and Information and Communications Technology (ICT) in higher level education.
The Design for All @eInclusion project investigated the current provision of education and training of future developers and associated disciplines and identified progress and gaps. Best practice included examples of specialist modules and âhidden gemsâ â instances of small elements such as single lectures that are optional, integrated or embedded within a larger module. These findings contributed to the development of curriculum guidelines which take account of the latest agreements for European harmonisation through the European Qualifications Framework. These guidelines are intended to stimulate the creation of new courses throughout Europe
Hamilton-Jacobi Theory and Information Geometry
Recently, a method to dynamically define a divergence function for a
given statistical manifold by means of the
Hamilton-Jacobi theory associated with a suitable Lagrangian function
on has been proposed. Here we will review this
construction and lay the basis for an inverse problem where we assume the
divergence function to be known and we look for a Lagrangian function
for which is a complete solution of the associated
Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to
replace probability distributions with probability amplitudes.Comment: 8 page
Asymptotics of Quantum Relative Entropy From Representation Theoretical Viewpoint
In this paper it was proved that the quantum relative entropy can be asymptotically attained by Kullback Leibler divergences of
probabilities given by a certain sequence of POVMs. The sequence of POVMs
depends on , but is independent of the choice of .Comment: LaTeX2e. 8 pages. The title was changed from "Asymptotic Attainment
for Quantum Relative Entropy
Asymptotics of Varadhan-type and the Gibbs Variational Principle
For a large class of quantum models of mean-field type the thermodynamic limit of the free energy density is proved to be given by the Gibbs variational principle. The latter is shown to be equivalent to a non-commutative version of Varadhanâs asymptotic formula
Equilibrium states and their entropy densities in gauge-invariant C*-systems
A gauge-invariant C*-system is obtained as the fixed point subalgebra of the
infinite tensor product of full matrix algebras under the tensor product
unitary action of a compact group. In the paper, thermodynamics is studied on
such systems and the chemical potential theory developed by Araki, Haag,
Kastler and Takesaki is used. As a generalization of quantum spin system, the
equivalence of the KMS condition, the Gibbs condition and the variational
principle is shown for translation-invariant states. The entropy density of
extremal equilibrium states is also investigated in relation to macroscopic
uniformity.Comment: 20 pages, revised in March 200
Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs
We prove multiplicativity of maximal output norm of classical noise
channels and thermal noise channels of arbitrary modes for all under the
assumption that the input signal states are Gaussian states. As a direct
consequence, we also show the additivity of the minimal output entropy and that
of the energy-constrained Holevo capacity for those Gaussian channels under
Gaussian inputs. To the best of our knowledge, newly discovered majorization
relation on symplectic eigenvalues, which is also of independent interest,
plays a central role in the proof.Comment: 9 pages, no figures. Published Versio
Free energy density for mean field perturbation of states of a one-dimensional spin chain
Motivated by recent developments on large deviations in states of the spin
chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the
variational expression of free energy density in the presence of a mean field
type perturbation. We extend their results from the product state case to the
Gibbs state case in the setting of translation-invariant interactions of finite
range. In the special case of a locally faithful quantum Markov state, we
clarify the relation between two different kinds of free energy densities (or
pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy
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