Quantum Cloning of Mixed States in Symmetric Subspace

Quantum cloning machine for arbitrary mixed states in symmetric subspace is proposed. This quantum cloning machine can be used to copy part of the output state of another quantum cloning machine and is useful in quantum computation and quantum information. The shrinking factor of this quantum cloning achieves the well-known upper bound. When the input is identical pure states, two different fidelities of this cloning machine are optimal.Comment: Revtex, 4 page

VORTICES AND MAGNETIZATION IN KAC'S MODEL

We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential $J_\gamma(i)=\gamma^2J(\gamma i)$, $J$ with compact support. The system is subject to boundary conditions with vorticity. Using a Glauber like dynamics, we compute minimizers of the free energy functional at low temperature, i.e. in the regime of phase transition. We have the numerical evidence of a vortex structure for minimizers, which present many common features with those of the Ginzburg-Landau functional

Induced gelation in a two-site spatial coagulation model

A two-site spatial coagulation model is considered. Particles of masses $m$ and $n$ at the same site form a new particle of mass $m+n$ at rate $mn$. Independently, particles jump to the other site at a constant rate. The limit (for increasing particle numbers) of this model is expected to be nondeterministic after the gelation time, namely, one or two giant particles randomly jump between the two sites. Moreover, a new effect of induced gelation is observed--the gelation happening at the site with the larger initial number of monomers immediately induces gelation at the other site. Induced gelation is shown to be of logarithmic order. The limiting behavior of the model is derived rigorously up to the gelation time, while the expected post-gelation behavior is illustrated by a numerical simulation.Comment: Published at http://dx.doi.org/10.1214/105051605000000755 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A generalised method for measuring weak lensing magnification with weighted number counts

We present a derivation of a generalized optimally-weighted estimator for the weak lensing magnification signal, including a calculation of errors. With this estimator, we present a local method for optimally estimating the local effects of magnification from weak gravitational lensing, using a comparison of number counts in an arbitrary region of space to the expected unmagnified number counts. We show that when equivalent lens and source samples are used, this estimator is simply related to the optimally-weighted correlation function estimator used in past work and vice-versa, but this method has the benefits that it can calculate errors with significantly less computational time, that it can handle overlapping lens and source samples, and that it can easily be extended to mass-mapping. We present a proof-of-principle test of this method on data from the CFHTLenS, showing that its calculated magnification signals agree with predictions from model fits to shear data. Finally, we investigate how magnification data can be used to supplement shear data in determining the best-fit model mass profiles for galaxy dark matter haloes. We find that at redshifts greater than z ~ 0.6, the inclusion of magnification can often significantly improve the constraints on the components of the mass profile which relate to galaxies' local environments relative to shear alone, and in high-redshift, low- and medium-mass bins, it can have a higher signal-to-noise than the shear signal.Comment: 20 pages, 10 figures, submitted to MNRAS, first revisio

Aprendizaje autónomo de redes neuronales artificiales

Estudiamos numéricamente redes neuronales artificiales multicapa con procesamiento unidireccional (feedforward) y su optimización con respecto a dos propiedades de especial importancia en el campo de las redes complejas y los modelos computacionales de sistemas biológicos: el cumplimiento de una función compleja con generalización de lo aprendido y la robustez estructural. En primer lugar, interesa optimizar las redes para cumplir cierta función: el reconocimiento de las vocales en una matriz de píxeles. Con ello, se espera no sólo que cada red sepa clasificar los patrones aprendidos, sino que pueda generalizar a casos novedosos lo que se le enseñó en casos particulares, clasificando correctamente las vocales aun cuando las señales que se le muestren presenten ruido o sean defectuosas. En segundo lugar, buscamos que las redes creadas sean estructuralmente robustas, esto es, conserven su buena operatividad luego de sufrir daños en su topología. Usualmente, para la optimización de redes neuronales artificiales, los algoritmos de aprendizaje que se emplean dependen de un agente externo implícito en su formulación que durante el proceso guía a la red en la modificación de sus parámetros hasta que ésta alcanza un desempeño satisfactorio u óptimo. La línea central de este trabajo es la implementación de un método estocástico de aprendizaje por refuerzo, denominado aprendizaje autónomo, según el cual el propio estado de la red define la magnitud y la dirección de los cambios para que ésta logre optimizarse.Fil: Bilen, Agustín Miguel. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales

Quantum measurement procedures via weak interactions

The general diagonal measurement A weak quantum measurement is a measurement for which any outcome does not disturb the quantum state more than a small amount ε. Weak measurements are universal: [OB05] showed one can construct a sequence of weak measurements that converge to any strong measurement using a random walk of weak measurement operators. Weak measurement walks via an interacting probe: We study possible realizations of a such a procedure when the weak measurement is effectuated via weak interaction of a probe with the system in question. Virtual measurements Given a desired measurement {M1, M2}, we construct a parametrized weak measurement {M±(x)} such that we achieve the desired measurement in the continuous limit lim δ→