Measuring the degree of unitarity for any quantum process

Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary one. The DU, as an intrinsic property of a given quantum process, is able to quantify the distance between the process and the group of unitary ones, and is closely related to the noise of this quantum process. We derive analytical results of DU for qubit unital channels, and obtain the lower and upper bounds in general. The lower bound is tight for most of quantum processes, and is particularly tight when the corresponding DU is sufficiently large. The upper bound is found to be an indicator for the tightness of the lower bound. Moreover, we study the distribution of DU in random quantum processes with different environments. In particular, The relationship between the DU of any quantum process and the non-markovian behavior of it is also addressed.Comment: 7 pages, 2 figure

Assessing Protein Conformational Sampling Methods Based on Bivariate Lag-Distributions of Backbone Angles

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model that should be considered to accurately parameterize the joint distribution of the angles? and What is the order of the local sequence–structure dependency that should be considered by a prediction method? We assess the model fits for different methods using bivariate lag-distributions of the dihedral/planar angles. Moreover, the main information across the lags can be extracted using a technique called Lag singular value decomposition (LagSVD), which considers the joint distribution of the dihedral/planar angles over different lags using a nonparametric approach and monitors the behavior of the lag-distribution of the angles using singular value decomposition. As a result, we developed graphical tools and numerical measurements to compare and evaluate the performance of different model fits. Furthermore, we developed a web-tool (http://www.stat.tamu.edu/∼madoliat/LagSVD) that can be used to produce informative animations

Magnetic Excitations in the High Tc Iron Pnictides

We calculate the expected finite frequency neutron scattering intensity based on the two-sublattice collinear antiferromagnet found by recent neutron scattering experiments as well as by theoretical analysis on the iron oxypnictide LaOFeAs. We consider two types of superexchange couplings between Fe atoms: nearest-neighbor coupling J1 and next-nearest-neighbor coupling J2. We show how to distinguish experimentally between ferromagnetic and antiferromagnetic J1. Whereas magnetic excitations in the cuprates display a so-called resonance peak at (pi,pi) (corresponding to a saddlepoint in the magnetic spectrum) which is at a wavevector that is at least close to nesting Fermi-surface-like structures, no such corresponding excitations exist in the iron pnictides. Rather, we find saddlepoints near (pi,pi/2) and (0,pi/2)(and symmetry related points). Unlike in the cuprates, none of these vectors are close to nesting the Fermi surfaces.Comment: 4 pages, 5 figure

Comment on 'Note on the dog-and-rabbit chase problem in introductory kinematics'

We comment on the recent paper by Yuan Qing-Xin and Du Yin-Xiao (Eur. J. Phys. 29 (2008) N43-N45).Comment: 2 pages, no figure