Complementarity and the algebraic structure of 4-level quantum systems

The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras. Complementary decompositions of a 4-level quantum system are described and a characterization of the Bell basis is obtained.Comment: 19 page

Maps on density operators preserving quantum f-divergences

For an arbitrary strictly convex function f defined on the non-negative real line we determine the structure of all transformations on the set of density operators which preserve the quantum f-divergence

Structure of sufficient quantum coarse-grainings

Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K). Assume that density matrices D_1 and D_2 acting on H are given. In the paper the consequences of the existence of a coarse-graining S from B(K) to B(H) satisfying ST(D_1)=D_1 and ST(D_2)=D_2 are given. (This condition means the sufficiency of T for D_1 and D_2.) Sufficiency implies a particular decomposition of the density matrices. This decomposition allows to deduce the exact condition for equality in the strong subadditivity of the von Neumann entropy.Comment: 13 pages, LATE

Covariance and Fisher information in quantum mechanics

Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasis that Fisher informations are obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.Comment: LATE

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 ‘hidden gems’ – 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

Hypothesis testing for Gaussian states on bosonic lattices

The asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons. A complete solution is provided for the problems of the Chernoff and the Hoeffding bounds and Stein's lemma in the case when both hypotheses are gauge-invariant Gaussian states with translation-invariant quasi-free parts.Comment: 22 pages, submitted versio

Stationary quantum source coding

In this paper the quantum source coding theorem is obtained for a completely ergodic source. This results extends Shannon's classical theorem as well as Schumacher's quantum noiseless coding theorem for memoryless sources. The control of the memory effects requires earlier results of Hiai and Petz on high probability subspaces.Comment: 8 page

A volume inequality for quantum Fisher information and the uncertainty principle

Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$det(Cov_\rho(A_h,A_j)) \geq det(- \frac{i}{2} Tr(\rho [A_h,A_j]))$$ gives a bound for the quantum generalized covariance in terms of the commutators $[A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $_{\rho,f}$ be the associated quantum Fisher information. In this paper we conjecture the inequality $$det (Cov_\rho(A_h,A_j)) \geq det (\frac{f(0)}{2} _{\rho,f})$$ that gives a non-trivial bound for any natural number $N$ using the commutators $i[\rho, A_h]$. The inequality has been proved in the cases $N=1,2$ by the joint efforts of many authors. In this paper we prove the case N=3 for real matrices