Essentially All Gaussian Two-Party Quantum States are a priori Nonclassical but Classically Correlated

Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon (quant-ph/9909044) have recently found necessary and sufficient conditions for the separability (classical correlation) of the Gaussian two-party (continuous variable) states. Duan et al remark that their criterion is based on a "much stronger bound" on the total variance of a pair of Einstein-Podolsky-Rosen-type operators than is required simply by the uncertainty relation. Here, we seek to formalize and test this particular assertion in both classical and quantum-theoretic frameworks. We first attach to these states the classical a priori probability (Jeffreys' prior), proportional to the volume element of the Fisher information metric on the Riemannian manifold of Gaussian (quadrivariate normal) probability distributions. Then, numerical evidence indicates that more than ninety-nine percent of the Gaussian two-party states do, in fact, meet the more stringent criterion for separability. We collaterally note that the prior probability assigned to the classical states, that is those having positive Glauber-Sudarshan P-representations, is less than one-thousandth of one percent. We, then, seek to attach as a measure to the Gaussian two-party states, the volume element of the associated (quantum-theoretic) Bures (minimal monotone) metric. Our several extensive analyses, then, persistently yield probabilities of separability and classicality that are, to very high orders of accuracy, unity and zero, respectively, so the two apparently quite distinct (classical and quantum-theoretic) forms of analysis are rather remarkably consistent in their findings.Comment: Seven pages, one table. Expanded introduction, additional references include

Uncertainty And Evolutionary Optimization: A Novel Approach

Evolutionary algorithms (EA) have been widely accepted as efficient solvers for complex real world optimization problems, including engineering optimization. However, real world optimization problems often involve uncertain environment including noisy and/or dynamic environments, which pose major challenges to EA-based optimization. The presence of noise interferes with the evaluation and the selection process of EA, and thus adversely affects its performance. In addition, as presence of noise poses challenges to the evaluation of the fitness function, it may need to be estimated instead of being evaluated. Several existing approaches attempt to address this problem, such as introduction of diversity (hyper mutation, random immigrants, special operators) or incorporation of memory of the past (diploidy, case based memory). However, these approaches fail to adequately address the problem. In this paper we propose a Distributed Population Switching Evolutionary Algorithm (DPSEA) method that addresses optimization of functions with noisy fitness using a distributed population switching architecture, to simulate a distributed self-adaptive memory of the solution space. Local regression is used in the pseudo-populations to estimate the fitness. Successful applications to benchmark test problems ascertain the proposed method's superior performance in terms of both robustness and accuracy.Comment: In Proceedings of the The 9th IEEE Conference on Industrial Electronics and Applications (ICIEA 2014), IEEE Press, pp. 988-983, 201

Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

Molecular modeling of intermolecular and intramolecular excluded volume interactions for polymers at interfaces

A hybrid modeling approach is proposed for inhomogeneous polymer solutions. The method is illustrated for the depletion problem with polymer chains up to N=103 segments in semidilute solutions and good solvent conditions. In a three-dimensional volume, a set of freely jointed chains is considered for which the translational degrees of freedom are sampled using a coarse grained Monte Carlo simulation and the conformational degrees of freedom of the chains are computed using a modified self-consistent field theory. As a result, both intramolecular and intermolecular excluded volume effects are accounted for, not only for chains near the surface, but in the bulk as well. Results are consistent with computer simulations and scaling considerations. More specifically, the depletion thickness, which is a measure for the bulk correlation length, scales as d~J-0.75 and converges to the mean field result in the concentrated regim