Structural approximations to positive maps and entanglement breaking channels

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.Comment: 18 pages, 3 figure

The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach

We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of 'noncommutative spaces' is the opposite of the category of C*-algebras. The second, loosely generalizing Stone duality, maintains that the category of 'pointfree spaces' is the opposite of the category of frames (i.e., complete lattices in which the meet distributes over arbitrary joins). One possible relationship between these two notions of space was unearthed by Banaschewski and Mulvey, who proved a constructive version of Gelfand duality in which the Gelfand spectrum of a commutative C*-algebra comes out as a pointfree space. Being constructive, this result applies in arbitrary toposes (with natural numbers objects, so that internal C*-algebras can be defined). Earlier work by the first three authors, shows how a noncommutative C*-algebra gives rise to a commutative one internal to a certain sheaf topos. The latter, then, has a constructive Gelfand spectrum, also internal to the topos in question. After a brief review of this work, we compute the so-called external description of this internal spectrum, which in principle is a fibered pointfree space in the familiar topos Sets of sets and functions. However, we obtain the external spectrum as a fibered topological space in the usual sense. This leads to an explicit Gelfand transform, as well as to a topological reinterpretation of the Kochen-Specker Theorem of quantum mechanics, which supplements the remarkable topos-theoretic version of this theorem due to Butterfield and Isham.Comment: 12 page

Interaction for Immersive Analytics

International audienceIn this chapter, we briefly review the development of natural user interfaces and discuss their role in providing human-computer interaction that is immersive in various ways. Then we examine some opportunities for how these technologies might be used to better support data analysis tasks. Specifically, we review and suggest some interaction design guidelines for immersive analytics. We also review some hardware setups for data visualization that are already archetypal. Finally, we look at some emerging system designs that suggest future directions

GB*-Algebras associated with inductive limits of Hilbert spaces

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Compatibility of observables represented by positive operator-valued measures

The proof of a result analogous to that in Koelman and de Muynck [Phys. Lett. A 98, 1 (1983)] is given for the case of unbounded observables. If two, not necessarily bounded, observables are represented by a positive operator-valued measure, then the measurement of any of them is undisturbed if and only if they commute. The Naimark theorem on dilations of spectral functions is exploited. A stronger version of Wigner's theorem is given.</p

Spectral trajectories,duality and inductive-projective limits of Hilbert spaces

An explicit representation of the topological dual of the inductive limit space H4 generated by a colllection R of s.a. operators, has been found in the form of a space of spectral trajectories. i.e .. vector-valued measures with the orthogonal scattering property. This paper is a continuation of (5) completing the previous theory. Illustrations of this type of spaces can be derived from distribution theory and Gel'fand triples theory. At the end of Section 5 we give a short summary on these matters

Influence of cutting conditions in turning with Wiper type inserts in surface roughness and cutting force

Dokonano oceny wpływu warunków obróbki na chropowatości powierzchni obrobionej oraz składowe całkowitej siły skrawania podczas toczenia stali węglowej C45.W badaniach zastosowano płytki skrawające z narożem promieniowym oraz płytki ostrzowe dogładzające typu Wiper. Oceny dokonano w oparciu o wyniki badań z zastosowaniem podawania cieczy obróbkowej w trybie obfitym, z minimalnym wydatkiem (MQL), przy użyciu schłodzonego sprężonego powietrza oraz bez udziału cieczy obróbkowej. Opisano stanowisko do pomiaru składowych całkowitej siły skrawania oraz przedstawiono metodykę pomiarów.In the paper, evaluation of the influence of selected cutting parameters on surface roughness of the workpiece is presented. Standard geometry and Wiper geometry inserts were applied. Relationship between cutting forces levels during turning tests of C45 steel are presented too. Moreover evaluation of experimental results which consider application of different strategies of cutting fluid supply such as: Minimal Quantity Lubrication, Cooled Compressed Air, Dry Machining are shown. Description of experimental conditions and methodology of investigation are presented. Finally experimental stands which were employed during surface roughness and cutting forces measurements are described too