Given two sets of quantum states {A1, . . . , Ak} and {B1, . . . , Bk}, represented as sets as density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T , represented as a trace-preserving completely positive map, such that T (Ai) = Bi for i = 1, . . . , k. General completely positive maps without the trace-preserving requirement, and un...

We give a hierarchy of many-parameter families of maps of the interval [0, 1] with an invariant measure and using the measure, we calculate Kolmogorov–Sinai entropy of these maps analytically. In contrary to the usual one-dimensional maps these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain region of pa...

This paper is motivated by the question “How can we produce the characteristics of a Wiener process (Brownian motion) from a semi-dynamical system?”. This question is intimately connected with Central Limit Theorems for non-invertible maps and various invariance principles. Many results on CLT and invariance principles for maps have been proved, see e.g. the surveys Denker [4] and Mackey and Ty...

Within the context of upcoming full-sky lensing surveys, the edge-preserving nonlinear algorithm Aski (All Sky κ Inversion) is presented. Using the framework of Maximum A Posteriori inversion, it aims at recovering the optimal full-sky convergence map from noisy surveys with masks. Aski contributes two steps: (i) CCD images of possibly crowded galactic fields are deblurred using automated edge-...

This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, stric...

A C-linear map θ (not necessarily bounded) between two Hilbert C-modules is said to be ‘orthogonality preserving’ if 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We prove that if θ is an orthogonality preserving map from a full Hilbert C0()-module E into another Hilbert C0()-module F that satisfies a weaker notion of C0()-linearity (called ‘localness’), then θ is bounded and there exists φ ∈ Cb()+...

A study of order preserving field automorphisms of ordered nonArchimedean field extensions of R will be presented. We show that, while the identity map is the only field automorphism of R, infinitely many nontrivial order preserving field automorphisms can be constructed on an ordered nonArchimedean field extension F of R. Moreover, we show that if P is an order preserving field automorphism of...