Optimal Image Reconstruction in Radio Interferometry

We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy techniques, but with an exact accounting of the multiplicity instead of the usual approximation involving Stirling's formula. It also incorporates an Occam factor, automatically limiting the effective amount of detail in the map to that justified by the data. We use Gibbs sampling to determine, to any desired degree of accuracy, the multi-dimensional posterior density distribution. From this we can construct a mean posterior map and other measures of the posterior density, including confidence limits on any well-defined function of the posterior map.Comment: 41 pages, 11 figures. High resolution figures 8 and 9 available at http://www.astro.uiuc.edu/~bwandelt/SuttonWandelt200

Advances in Calibration and Imaging Techniques in Radio Interferometry

This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework has a number of benefits, ranging from clarification of the fundamentals, use of standard numerical optimization techniques, and generalization or specialization to new algorithms

Entangling characterization of (SWAP)1/m and Controlled unitary gates

We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.Comment: 12 pages, 1 figure, One more paragraph added in Introductio

Mosaicking with cosmic microwave background interferometers

Measurements of cosmic microwave background (CMB) anisotropies by interferometers offer several advantages over single-dish observations. The formalism for analyzing interferometer CMB data is well developed in the flat-sky approximation, valid for small fields of view. As the area of sky is increased to obtain finer spectral resolution, this approximation needs to be relaxed. We extend the formalism for CMB interferometry, including both temperature and polarization, to mosaics of observations covering arbitrarily large areas of the sky, with each individual pointing lying within the flat-sky approximation. We present a method for computing the correlation between visibilities with arbitrary pointing centers and baselines and illustrate the effects of sky curvature on the l-space resolution that can be obtained from a mosaic.Comment: 9 pages; submitted to Ap

Displacement- and Timing-Noise Free Gravitational-Wave Detection

Motivated by a recently-invented scheme of displacement-noise-free gravitational-wave detection, we demonstrate the existence of gravitational-wave detection schemes insusceptible to both displacement and timing (laser) noises, and are thus realizable by shot-noise-limited laser interferometry. This is possible due to two reasons: first, gravitational waves and displacement disturbances contribute to light propagation times in different manners; second, for an N-detector system, the number of signal channels is of the order O(N^2), while the total number of timing- and displacement-noise channels is of the order O(N).Comment: 4 pages, 3 figures; mistake correcte

Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems

The use of d-state systems, or qudits, in quantum information processing is discussed. Three-state and higher dimensional quantum systems are known to have very different properties from two-state systems, i.e., qubits. In particular there exist qudit states which are not equivalent under local unitary transformations unless a selection rule is violated. This observation is shown to be an important factor in the theory of decoherence-free, or noiseless, subsystems. Experimentally observable consequences and methods for distinguishing these states are also provided, including the explicit construction of new decoherence-free or noiseless subsystems from qutrits. Implications for simulating quantum systems with quantum systems are also discussed.Comment: 13 pages, 1 figures, Version 2: Typos corrected, references fixed and new ones added, also includes referees suggested changes and a new exampl

Density matrix numerical renormalization group for non-Abelian symmetries

We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian, local symmetries present in the quantum impurity system. We illustrate the benefits of using non-Abelian symmetries by the example of calculations for the T-matrix of the two-channel Kondo model in the presence of magnetic field, for which conventional NRG methods produce large errors and/or take a long run-time.Comment: 12 pages, 6 figures, PRB forma

Microarcsecond Radio Imaging using Earth Orbit Synthesis

The observed interstellar scintillation pattern of an intra-day variable radio source is influenced by its source structure. If the velocity of the interstellar medium responsible for the scattering is comparable to the earth's, the vector sum of these allows an observer to probe the scintillation pattern of a source in two dimensions and, in turn, to probe two-dimensional source structure on scales comparable to the angular scale of the scintillation pattern, typically $\sim 10 \mu$as for weak scattering. We review the theory on the extraction of an ``image'' from the scintillation properties of a source, and show how earth's orbital motion changes a source's observed scintillation properties during the course of a year. The imaging process, which we call Earth Orbit Synthesis, requires measurements of the statistical properties of the scintillations at epochs spread throughout the course of a year.Comment: ApJ in press. 25 pages, 7 fig

Unpolarized light in quantum optics

We present a new derivation of the unpolarized quantum states of light, whose general form was first derived by Prakash and Chandra [Phys. Rev. A 4, 796 (1971)]. Our derivation makes use of some basic group theory, is straightforward, and offers some new insights.Comment: 3 pages, REVTeX, presented at ICQO'200

Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra E6

The quantum trigonometric Calogero-Sutherland models related to Lie algebras admit a parametrization in which the dynamical variables are the characters of the fundamental representations of the algebra. We develop here this approach for the case of the exceptional Lie algebra E6.Comment: 17 pages, no figure