Measurement in control and discrimination of entangled pairs under self-distortion

Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume these resources stable and not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. for quantum computation or quantum cryptography). Experimental work shows how to produce entangled spin qubits in quantum dots and electron gases, so its identification and control are crucial for later applications. The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or, just to try of reconstruct it using some procedures which do not alter their quantum nature. Two different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field which becoming self-distorted, can be reconstructed without previous discrimination by adding an external magnetic field, with fidelity close to 1 (with respect to the original state, but without discrimination). After, each state can be more efficiently discriminated. The aim of this work is to show how combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it's possible a) improve the discrimination, and b) reprepare faithfully the original states. The complete process gives fidelities better than 0.9. In the meanwhile, some results about a class of equivalence for the required measurements were found. This property lets us select the adequate measurement in order to ease the repreparation after of discrimination, without loss of entanglement.Comment: 6 figure

Testing the equality of nonparametric regression curves

This paper proposes a test for the equality of nonparametric regression curves that does not depend on the choice of a smoothing number. The test statistic is a weighted empirical process easy to compute. It is powerful under alternatives that converge to the null at a rate n­½. The disturbance distributions are arbitrary and possibly unequal, and conditions on the regressors distribution are very mild. A simulation study demonstrates that the test enjoys good level and power properties in small samples. We also study extensions to multiple regression, and testing the equality of several regression curves

Testing serial independence using the sample distribution function

This paper presents and discusses a nonparametric test for detecting serial dependence. We consider a Cramèr-v.Mises statistic based on the difference between the joint sample distribution and the product of the marginals. Exact critical values can be approximated from the asymptotic null distribution or by resampling, randomly permuting the original series. The approximation based on resampling is more accurate and the corresponding test enjoys, like other bootstrap based procedures, excellent level accuracy, with level error of order T-3/2. A Monte Carlo experiment illustrates the test performance with small and moderate sample sizes. The paper also includes an application, testing the random walk hypothesis of exchange rate returns for several currencies

Computing Nonparametric Functional Estimates in Semiparametric Problems

The purpose of this note is to provide a brief account of available FORTRAN Routines for computing nonparametric functional estimates, Frequently used in semiparametric problems, evaluated at each data point. Then semiparametric estimates can be computed employing the use-favored economic software.Publicad

Specification testing

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The New SI and the Fundamental Constants of Nature

The launch in 2019 of the new international system of units is an opportunity to highlight the key role that the fundamental laws of physics and chemistry play in our lives and in all the processes of basic research, industry and commerce. The main objective of these notes is to present the new SI in an accessible way for a wide audience. After reviewing the fundamental constants of nature and its universal laws, the new definitions of SI units are presented using, as a unifying principle, the discrete nature of energy, matter and information in these universal laws. The new SI system is here to stay: although the experimental realizations may change due to technological improvements, the definitions will remain unaffected. Quantum metrology is expected to be one of the driving forces to achieve new quantum technologies of the second generation. ----- La puesta en marcha en 2019 del nuevo sistema internacional de unidades es una oportunidad para resaltar el papel fundamental que las leyes fundamentales de la F\'{\i}sica y la Qu\'{\i}mica juegan en nuestra vida y en todos los procesos de la investigaci\'on fundamental, la industria y el comercio. El principal objetivo de estas notas es presentar el nuevo SI de forma accesible para una audiencia amplia. Tras repasar las constantes fundamentales de la naturaleza y sus leyes universales, se presentan las nuevas definiciones de las unidades SI utilizando como principio unificador la naturaleza discreta de la energ\'{\i}a, la materia y la informaci\'on en esas leyes universales. El nuevo sistema SI tiene vocaci\'on de futuro: aunque las realizaciones experimentales cambien por mejoras tecnol\'gicas, las definiciones permanecer\'an inalteradas. La Metrolog\'{\i}a cu\'antica est\'a llamada a ser uno de las fuerzas motrices para conseguir nuevas tecnolog\'{\i}as cu\'anticas de segunda generaci\'on.Comment: Revtex file, color figures. English version y en espa\~no

The Critical Point of Unoriented Random Surfaces with a Non-Even Potential

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double-scaling limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a cuartic interaction.Comment: 20p (Frontpage included