Products of Random Matrices

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.Comment: 9 pages, 1 figur

The WIYN Open Cluster Study Photometric Binary Survey: Initial Findings for NGC 188

The WIYN open cluster study (WOCS) has been working to yield precise magnitudes in the Johnson-Kron-Cousins UBVRI system for all stars in the field of a selection of ``prototypical'' open clusters. Additionally, WOCS is using radial velocities to obtain orbit solutions for all cluster binary stars with periods of less than 1000 days. Recently, WOCS is being expanded to include the near-infrared JHK_s (deep ground-based plus 2MASS) and mid-infrared ([3.6], [4.5], [5.8], [8.0]) photometry from Spitzer/IRAC observations. This multi-wavelength data (0.3--8.0 microns) allows us photometrically to identify binaries, with mass ratios from 1.0--0.3, across a wide range of primary masses. The spectral energy distribution (SED) fitter by Robitaille et al. (2007) is used to fit the fluxes of 10--12 bands, converted from the observed magnitudes, to Kurucz stellar models. Using this photometric technique, we find that NGC 188 has a binary fraction of 36--49% and provide a star-by-star comparison to the WOCS radial velocity-based binary study.Comment: 2 pages, 2 figures, Conference Proceedings from "Dynamical Evolution of Dense Stellar Systems'', IAU Symposium 246, Eds. E. Vesperini, M. Giersz, & A. Sill

Direct Characterization of Quantum Dynamics

The characterization of quantum dynamics is a fundamental and central task in quantum mechanics. This task is typically addressed by quantum process tomography (QPT). Here we present an alternative "direct characterization of quantum dynamics" (DCQD) algorithm. In contrast to all known QPT methods, this algorithm relies on error-detection techniques and does not require any quantum state tomography. We illustrate that, by construction, the DCQD algorithm can be applied to the task of obtaining partial information about quantum dynamics. Furthermore, we argue that the DCQD algorithm is experimentally implementable in a variety of prominent quantum information processing systems, and show how it can be realized in photonic systems with present day technology.Comment: 4 pages, 2 figures, published versio

The trumping relation and the structure of the bipartite entangled states

The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new results. Most notably, we show that the dimension of the required catalyst is in general unbounded; there is no integer $k$ such that it suffices to consider catalysts of dimension $k$ or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.Comment: 7 pages, RevTe

Novel schemes for measurement-based quantum computation

We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique further develops tools from many-body physics - based on finitely correlated or projected entangled pair states - to go beyond the cluster-state based one-way computer. We identify resource states that are radically different from the cluster state, in that they exhibit non-vanishing correlation functions, can partly be prepared using gates with non-maximal entangling power, or have very different local entanglement properties. In the computational models, the randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. Finally, we comment on the possibility of tailoring computational models to specific physical systems as, e.g. cold atoms in optical lattices.Comment: 5 pages RevTeX, 1 figure, many diagrams. Title changed, presentation improved, material adde

Follow up on the crystal growth experiments of the LDEF

The results of the 4 solution growth experiments on the LDEF have been published elsewhere. Both the crystals of CaCO3, which were large and well shaped, and the much smaller TTF-TCNQ crystals showed unusual morphological behavior. The follow up on these experiments was begun in 1981, when ESA initiated a 'Concept Definition Study' on a large, 150 kg, Solution Growth Facility (SGF) to be included in the payload of EURECA-1, the European Retrievable Carrier. This carrier was a continuation of the European Spacelab and at that time planned for launch in 1987. The long delay of the LDEF retrieval and of subsequent missions brought about reflections both on the concept of crystal growth in space and on the choice of crystallization materials that had been made for the LDEF. Already before the LDEF retrieval, research on TTF-TCNQ had been stopped, and a planned growth experiment with TTF-TCNQ on the SGF/EURECA had been cancelled. The target of the SGF investigation is now more fundamental in nature. None of the crystals to be grown here are, like TTF-TCNQ, in particular demand by science or industry, and the crystals only serve the purpose of model crystals. The real purpose of the investigation is to study the growth behavior. One of the experiments, the Soret Coefficient Measurement experiment is not growing crystals at all, but has it as its sole purpose to obtain accurate information on thermal diffusion, a process of importance in crystal growth from solution

Useful entanglement can be extracted from all nonseparable states

We consider entanglement distillation from a single-copy of a multipartite state, and instead of rates we analyze the "quality" of the distilled entanglement. This "quality" is quantified by the fidelity with the GHZ-state. We show that each not fully-separable state $\sigma$ can increase the "quality" of the entanglement distilled from other states, no matter how weakly entangled is $\sigma$. We also generalize this to the case where the goal is distilling states different than the GHZ. These results provide new insights on the geometry of the set of separable states and its dual (the set of entanglement witnesses).Comment: 7 page

Optimality of programmable quantum measurements

We prove that for a programmable measurement device that approximates every POVM with an error $\le \delta$, the dimension of the program space has to grow at least polynomially with $\frac{1}{\delta}$. In the case of qubits we can improve the general result by showing a linear growth. This proves the optimality of the programmable measurement devices recently designed in [G. M. D'Ariano and P. Perinotti, Phys. Rev. Lett. \textbf{94}, 090401 (2005)]