The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity, written in terms of over-complete sets of rank-one projectors and of associated Gram-Schmidt operators taking into account their non-orthogonality, are then use...

Deformable template representations of observed imagery, model the variability of target pose via the actions of the matrix Lie groups on rigid templates. In this paper, we study the construction of minimum mean squared error estimators on the special orthogonal group, SO(n), for pose estimation. Due to the nonflat geometry of SO(n), the standard Bayesian formulation, of optimal estimators and ...

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

Ruth Curtain Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands. E-mail:[email protected], Kalle Mikkola Helsinki University of Technology, Institute of Mathematics, Box 1100, 02015 HUT, Finland. E-mail:[email protected], Amol Sasane Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom....

We study a renormalization group (RG) map for tensor networks that include two-dimensional lattice spin systems such as the Ising model. Numerical studies of RG maps have been quite successful at reproducing known critical behavior. In those numerical must be truncated to keep dimension legs tensors bounded. Our act on an infinite-dimensional Hilbert space, and our does not involve any truncati...

The Hooman{Wielandt inequality which gives a bound for the distance between the spectra of two normal matrices, is generalized to normal operators A; B on a separable Hilbert space, such that A ? B is Hilbert{Schmidt.

Dedicated to the memory of Al Cliiord, a wonderful mathematician and a wonderful man. Abstract Of concern are semigroups of linear norm one operators on Hilbert space of the form (discrete case) T = fT n : n = 0; 1; 2; g or (continuous case) T = fT (t) : t 0g: Using ergodic theory and Hilbert-Schmidt operators, the Cess aro limits (as n! 1) of j< T n f; f >j 2 ; j< T (n)f; f >j 2 are computed (...

the purpose of the present study is to introduce the sequence space[{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},]where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. the topological properties and inclusion relations of this space are studied. moreover, the prob...

As classical information arises from probability correlation between two random variables, quantum information arises from entanglement [1, 2]. Motivated by the finding of an entangled state which does not violate Bell’s inequality, the problem of quantifying entanglement has received an increasing interest recently. Vedral et. al. [3] proposed three necessary conditions that any measure of ent...