The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C ⊗ C whose operatorSchmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C ⊗ C with operatorSchmidt number S for every S ∈ {1, ..., 9}. This corollary...

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases. Then we construct Bessel sequences frames and Riesz bases for the class of Hilbert Schmidt operators using the tensor product of such sequences in the original...

Christoph Stahl a,*, Bernd Krieg-Brückner a, Wolfgang Zagler b and Björn Göttfried c a Cyber-Physical Systems, German Research Center for Artificial Intelligence, DFKI GmbH, Enrique-Schmidt-Straße 5, D-28359 Bremen, Germany b Institut für Gestaltungsund Wirkungsforschung, Zentrum für Angewandte Assistierende Technologien, Favoritenstraße 11/187-2b, A-1040 Wien, Austria c Artificial Intelligence...

The first platynine ground beetle, Limodromus hoffeinsorum sp. n., is described from Baltic amber at species level. The fossil species is considered the sister taxon of the modern species group of L. assimilis (Paykull, 1790). However, it was adapted to warmer climate conditions. The habitat of the new species is assumed similar to that of the modern L. klausnitzeri Schmidt, 2005, which represe...

In this article we study convexity properties of distance functions in infinite dimensional Finsler unitary groups, such as the full group, Schatten perturbations identity and groups finite von Neumann algebras. The structures are defined by translation different norms on tangent space at identity. We first prove a result for metric derived from operator norm group. also strong results squared ...

We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product locally compact Abelian group G with its dual $${\hat{G}}$$ . The method is based upon Pontryagin duality allowing to establish an isometrical isomorphism between space Hilbert–Schmidt operators in $$L^2(G)$$ and Hilbert $$L^2({\hat{G}}\times G)$$ Any such determines pair ...

AIM To compare higher order aberrations in two aspherical intraocular lenses (IOLs): Akreos advanced optics (AO) and Dr. Schmidt Microcrystalline 6125 aspheric anterior surface (MC6125AS) with each other. METHODS Forty eyes of 39 patients underwent phacoemulsification and Akreos AO and MC6125AS were implanted in their eyes in a random manner. Three months post-operatively, higher order aberra...

The Spheres of Influence, “Assessing Assays” (Schmidt 2002), in the May 2002 issue of EHP criticizes the National Toxicology Program rodent bioassay (NTPRB) without discussing its importance in regulation and public health. The Spheres article (Schmidt 2002) does not express concern for the validity of alternative transgenic methods proposed to replace the NTPRB for detecting carcinogens. By fo...