Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime dimension N is given by exploiting the finite Heisenberg group (also called the Pauli group) and the action of SL(2,Z_N) on finite phase space Z_N x Z_N implemented by unitary operators in the Hilbert space. Crucial for the proof is that, for prime N, Z_N is also a finite field.Comment: 13 pages; accepted in J. Phys. A: Math. Theo

Unapređenje vijabilnosti i stabilnosti probiotskog proizvoda sa Saccharomyces boulardii DBVPG

In recent decades, probiotic products have been increasingly used to prevent certain gastrointestinal and urogenital disorders, to improve the general condition of the body and as a supplement to pharmacological therapy. They are most often registered as dietary supplements, and less often as drugs in the form of capsules, powders, and solutions. Optimization of technological processes of production and packaging of these products aims to maintain probiotic characteristics while adhering to all criteria during production that ensure quality, bioavailability and optimal therapeutic effects. In this paper, the importance of choosing primary and secondary packaging materials was explored with the aim of preserving the viability of probiotic cells in capsules for two years, i.e. during the shelf life. By comparing the applications of polyvinyl chloride (PVC) and PVC/polyvinylidene chloride/polyethylene blister foils, better protection of probiotic cells was observed by applying the multilayer foil. In addition, in this research, further improvements of probiotic cell protection were achieved by applying a secondary packing-flow pack bag with inert gas for storing multilayered blisters.Probiotski proizvodi se poslednjih decenija sve više koriste za prevenciju određenih gastrointestinalnih i urogenitalnih poremećaja, za poboljšanje opšteg stanja organi-zma i kao dopuna farmakološke terapije. Najčešće su registrovani kao dijetetski suple-menti, a ređe kao lekovi u obliku kapsula, praškova i rastvora. Optimizacija tehnoloških procesa proizvodnje i pakovanje ovih proizvoda ima za cilj održavanje probiotskih karakteristika uz istovremeno pridržavanje svih kriterijuma u toku proizvodnje koji osiguravaju kvalitet, biološku raspoloživost i optimalno terapijsko dejstvo U ovom radu razmatran je značaj izbora primarnog i sekundarnog materijala za pakovanje sa ciljem očuvanja vijabilnost probiotskih ćelija u kapsulama tokom dve godine tj. tokom roka upotrebe. Poređenjem primene PVC (polivinil hlorid) i PVC/poliviniliden hlorid/poli-etilen (PVC/PVdC/PE) blister folija uočena je bolja zaštita probotskih ćelija od kiseonika i vlage primenom višeslojene folije. Dodatne efekte zaštite probiotskih ćelija u ovom radu potvrdjene su primenom dodatne zaštite blistera upotrebom sekundarnog pakovanja (engl. flow pack) kesice sa inertni gasom

Invariant information and quantum state estimation

The invariant information introduced by Brukner and Zeilinger, Phys. Rev. Lett. 83, 3354 (1999), is reconsidered from the point of view of quantum state estimation. We show that it is directly related to the mean error of the standard reconstruction from the measurement of a complete set of mutually complementary observables. We give its generalization in terms of the Fisher information. Provided that the optimum reconstruction is adopted, the corresponding quantity loses its invariant character.Comment: 4 pages, no figure

Numerical analysis of temperature field during hardfacing process and comparison with experimental results

The three-dimensional transient nonlinear thermal analysis of the hard facing process is performed by using the finite element method. The simulations were executed on the open source Salome platform using the open source finite element solver Code_Aster. The Gaussian double ellipsoid was selected in order to enable greater possibilities for the calculation of the moving heat source. The numerical results were compared with available experimental results

Wigner Functions and Separability for Finite Systems

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of dimension p^n where p is a prime number. With this limitation it is possible to define a phase space and Wigner functions in close analogy to the continuous case. That is, we use a phase space that is a direct sum of n two-dimensional vector spaces each containing p^2 points. This is in contrast to the more usual choice of a two-dimensional phase space containing p^(2n) points. A useful aspect of this approach is that we can relate complete separability of density matrices and their Wigner functions in a natural way. We discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd. Special attention is required for two qubits (p=2) and our technique fails to establish the separability property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of the A matrices has been adde

Affine Constellations Without Mutually Unbiased Counterparts

It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those of mutually unbiased constellations, mostly in dimension six. The observed discrepancies make a deeper relation between the two existence problems unlikely.Comment: 8 page

First Report of Botrytis Blight Caused by Botrytis cinerea on Paeonia lactiflora in Serbia

Paeonia lactiflora Pall. (herbaceous peony), a perennial flower, has been grown worldwide in gardens and landscapes. Peony plants cv. Sarah Bernard with leaf blight were observed in two home gardens located in Jagodina, central Serbia. To our knowledge, this is the first report of Botrytis blight on P. lactiflora in Serbia

Simultaneous measurement of coordinate and momentum on a von Neumann lattice

It is shown that on a finite phase plane the $kq$-coordinates and the sites of a von Neumann lattice are conjugate to one another. This elementary result holds when the number $M$ defining the size of the phase plane can be expressed as a product, $M=M_{1}M_{2}$, with $M_{1}$ and $M_{2}$ being relatively prime. As a consequence of this result a hitherto unknown wave function is defined giving the probability of simultaneously measuring the momentum and coordinate on the von Neumann lattice.Comment: Published in EPL 83 (2008) 1000

Certainty relations between local and nonlocal observables

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.Comment: 4 pages, no figure