Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

A Schmidt number for density matrices

We introduce the notion of a Schmidt number of a bipartite density matrix, characterizing the minimum Schmidt rank of the pure states that are needed to construct the density matrix. We prove that Schmidt number is nonincreasing under local quantum operations and classical communication. We show that $k$-positive maps witness Schmidt number, in the same way that positive maps witness entanglement. We show that the family of states which is made from mixing the completely mixed state and a maximally entangled state have increasing Schmidt number depending on the amount of maximally entangled state that is mixed in. We show that Schmidt number {\it does not necessarily increase} when taking tensor copies of a density matrix $\rho$; we give an example of a density matrix for which the Schmidt numbers of $\rho$ and $\rho \otimes \rho$ are both 2.Comment: 5 pages RevTex, 1 typo in Proof Lemma 1 correcte

Shrinking a large dataset to identify variables associated with increased risk of Plasmodium falciparum infection in Western Kenya

Large datasets are often not amenable to analysis using traditional single-step approaches. Here, our general objective was to apply imputation techniques, principal component analysis (PCA), elastic net and generalized linear models to a large dataset in a systematic approach to extract the most meaningful predictors for a health outcome. We extracted predictors for Plasmodium falciparum infection, from a large covariate dataset while facing limited numbers of observations, using data from the People, Animals, and their Zoonoses (PAZ) project to demonstrate these techniques: data collected from 415 homesteads in western Kenya, contained over 1500 variables that describe the health, environment, and social factors of the humans, livestock, and the homesteads in which they reside. The wide, sparse dataset was simplified to 42 predictors of P. falciparum malaria infection and wealth rankings were produced for all homesteads. The 42 predictors make biological sense and are supported by previous studies. This systematic data-mining approach we used would make many large datasets more manageable and informative for decision-making processes and health policy prioritization

Angular Schmidt Modes in Spontaneous Parametric Down-Conversion

We report a proof-of-principle experiment demonstrating that appropriately chosen set of Hermite-Gaussian modes constitutes a Schmidt decomposition for transverse momentum states of biphotons generated in the process of spontaneous parametric down conversion. We experimentally realize projective measurements in Schmidt basis and observe correlations between appropriate pairs of modes. We perform tomographical state reconstruction in the Schmidt basis, by direct measurement of single-photon density matrix eigenvalues.Comment: 5 pages, 4 figure

Character of Locally Inequivalent Classes of States and Entropy of Entanglement

In this letter we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exist infinite number of deterministically locally inequivalent classes of pure bipartite states in the same Schmidt rank (starting from three) having same amount of entanglement. Further, if there exists incomparable states with same entanglement in higher Schmidt ranks (greater than three), then they should differ in at least three Schmidt coefficients.Comment: 4 pages, revtex4, no figure, accepted in Physical Review A (rapid communications

Schmidt Analysis of Pure-State Entanglement

We examine the application of Schmidt-mode analysis to pure state entanglement. Several examples permitting exact analytic calculation of Schmidt eigenvalues and eigenfunctions are included, as well as evaluation of the associated degree of entanglement.Comment: 5 pages, 3 figures, for C.M. Bowden memoria

Effect of Schmidt number on the velocity–scalar cospectrum in isotropic turbulence with a mean scalar gradient

We consider transport of a passive scalar by an isotropic turbulent velocity field in the presence of a mean scalar gradient. The velocity–scalar cospectrum measures the distribution of the mean scalar flux across scales. An inequality is shown to bound the magnitude of the cospectrum in terms of the shell-summed energy and scalar spectra. At high Schmidt number, this bound limits the possible contribution of the sub-Kolmogorov scales to the scalar flux. At low Schmidt number, we derive an asymptotic result for the cospectrum in the inertial–diffusive range, with a -11/3 power law wavenumber dependence, and a comparison is made with results from large-eddy simulation. The sparse direct-interaction perturbation (SDIP) is used to calculate the cospectrum for a range of Schmidt numbers. The Lumley scaling result is recovered in the inertial–convective range and the constant of proportionality was calculated. At high Schmidt numbers, the cospectrum is found to decay exponentially in the viscous–convective range, and at low Schmidt numbers, the -11/3 power law is observed in the inertial–diffusive range. Results are reported for the cospectrum from a direct numerical simulation at a Taylor Reynolds number of 265, and a comparison is made at Schmidt number order unity between theory, simulation and experiment

On the Contractivity of Hilbert-Schmidt distance under open system dynamics

We show that the Hilbert-Schmidt distance, unlike the trace distance, between quantum states is generally not monotonic for open quantum systems subject to Lindblad semigroup dynamics. Sufficient conditions for contractivity of the Hilbert-Schmidt norm in terms of the dissipation generators are given. Although these conditions are not necessary, simulations suggest that non-contractivity is the typical case, i.e., that systems for which the Hilbert-Schmidt distance between quantum states is monotonically decreasing form only a small set of all possible dissipative systems for N>2, in contrast to the case N=2 where the Hilbert-Schmidt distance is always monotonically decreasing.Comment: Major revision. We would particularly like to thank D Perez-Garcia for constructive feedbac

Some remarks about the positivity of random variables on a Gaussian probability space

Let $(W,H,\mu)$ be an abstract Wiener space and $L$ be a probability density of class LlogL. Using the measure transportation of Monge-Kantorovitch, we prove that the kernel of the projection of L on the second Wiener chaos defines an (Hilbert-Schmidt) operator which is lower bounded by another Hilbert-Schmidt operator.Comment: 6 page