Notes on coarse grainings and functions of observables

Using the Naimark dilation theory we investigate the question under what conditions an observable which is a coarse graining of another observable is a function of it. To this end, conditions for the separability and for the Boolean structure of an observable are given

Two questions on quantum statistics

The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the probability measure. Differential operators are shown to lead to physically relevant cases where the expectation values of large classes of noncommuting observables do not distinguish superpositions of states and, in particular, where the full moment information does not determine the probability measure.Comment: 8 page

The norm-1-property of a quantum observable

A normalized positive operator measure $X\mapsto E(X)$ has the norm-1-property if \no{E(X)}=1 whenever $E(X)\ne O$. This property reflects the fact that the measurement outcome probabilities for the values of such observables can be made arbitrary close to one with suitable state preparations. Some general implications of the norm-1-property are investigated. As case studies, localization observables, phase observables, and phase space observables are considered.Comment: 14 page

Complementary Observables in Quantum Mechanics

We review the notion of complementarity of observables in quantum mechanics, as formulated and studied by Paul Busch and his colleagues over the years. In addition, we provide further clarification on the operational meaning of the concept, and present several characterisations of complementarity - some of which new - in a unified manner, as a consequence of a basic factorisation lemma for quantum effects. We work out several applications, including the canonical cases of position-momentum, position-energy, number-phase, as well as periodic observables relevant to spatial interferometry. We close the paper with some considerations of complementarity in a noisy setting, focusing especially on the case of convolutions of position and momentum, which was a recurring topic in Paul's work on operational formulation of quantum measurements and central to his philosophy of unsharp reality

Moment operators of the Cartesian margins of the phase space observables

The theory of operator integrals is used to determine the moment operators of the Cartesian margins of the phase space observables generated by the mixtures of the number states. The moments of the $x$-margin are polynomials of the position operator and those of the $y$-margin are polynomials of the momentum operator.Comment: 14 page

The uniqueness question in the multidimensional moment problem with applications to phase space observables

The theory of holomorphic functions of several complex variables is applied in proving a multidimensional variant of a theorem involving an exponential boundedness criterion for the classical moment problem. A theorem of Petersen concerning the relation between the multidimensional and one-dimensional moment problems is extended for half-lines and compact subsets of the real line. These results are used to solve the moment problem for the quantum phase space observables generated by the number states.Comment: 13 pages, submitted to Reports on Mathematical Physic

Positive sesquilinear form measures and generalized eigenvalue expansions

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized eigenvalue type expansions. Though there are formal similarities with earlier approaches to special cases of the problem, the paper differs e.g. from standard rigged Hilbert space constructions and avoids the introduction of nuclear spaces. The techniques are predominantly measure theoretic and hence the Hilbert spaces involved are separable. The results range from a Naimark type dilation result to direct integral representations and a fairly concrete generalized eigenvalue expansion for unbounded normal operators.Comment: 23 pages, to appear in J. Math. Anal. App

The Finnish Biodiversity Information Facility as a best-practice model for biodiversity data infrastructures

Biodiversity informatics has advanced rapidly with the maturation of major biodiversity data infrastructures (BDDIs), such as the Global Biodiversity Information Facility sharing unprecedented data volumes. Nevertheless, taxonomic, temporal and spatial data coverage remains unsatisfactory. With an increasing data need, the global BDDIs require continuous inflow from local data mobilisation, and national BDDIs are being developed around the world. The global BDDIs are specialised in certain data types or data life cycle stages which, despite possible merits, renders the BDDI landscape fragmented and complex. That this often is repeated at the national level creates counterproductive redundancy, complicates user services, and frustrates funders. Here, we present the Finnish Biodiversity Information Facility (FinBIF) as a model of an all-inclusive BDDI. It integrates relevant data types and phases of the data life cycle, manages them under one IT architecture, and distributes the data through one service portal under one brand. FinBIF has experienced diverse funder engagement and rapid user uptake. Therefore, we suggest the integrated and inclusive approach be adopted in national BDDI development.peerReviewe

Review of LTCC technology for millimeter waves and photonics

VTT Technical Research Centre of Finland Ltd. has developed and utilized Low Temperature Co-fired Ceramic (LTCC) technology for about 25 years. This paper presents our activities related to photonics and millimetre-waves, including also a relevant literature survey. First a short summary of the technology is given. Especially, the unique features of LTCC technology are described in more details. In addition, several examples have been given to show the validity of LTCC technology in these high-performance fields