42 research outputs found
Quantum tomography via equidistant states
We study the possibility of performing quantum state tomography via
equidistant states. This class of states allows us to propose a non-symmetric
informationally complete POVM based tomographic scheme. The scheme is defined
for odd dimensions and involves an inversion which can be analytically carried
out by Fourier transform
Correlation Functions of Dense Polymers and c=-2 Conformal Field Theory
The model of dense lattice polymers is studied as an example of non-unitary
Conformal Field Theory (CFT) with . ``Antisymmetric'' correlation
functions of the model are proved to be given by the generalized Kirchhoff
theorem. Continuous limit of the model is described by the free complex
Grassmann field with null vacuum vector. The fundamental property of the
Grassmann field and its twist field (both having non-positive conformal
weights) is that they themselves suppress zero mode so that their correlation
functions become non-trivial. The correlation functions of the fields with
positive conformal weights are non-zero only in the presence of the Dirichlet
operator that suppresses zero mode and imposes proper boundary conditions.Comment: 5 pages, REVTeX, remark is adde
Array algorithms for H^2 and H^∞ estimation
Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms
Locally definitizable operators: the local structure of the spectrum
We consider different types of spectral points of locally definitizable operators which can be defined with the help of approximate eigensequences. Their behavior allow a characterization in terms of the (local) spectral function. Moreover, we review some perturbation results for locally definitizable operators