Spatial structures and localization of vacuum entanglement in the linear harmonic chain

We study the structure of vacuum entanglement for two complimentary segments of a linear harmonic chain, applying the modewise decomposition of entangled gaussian states discussed in \cite {modewise}. We find that the resulting entangled mode shape hierarchy shows a distinctive layered structure with well defined relations between the depth of the modes, their characteristic wavelength, and their entanglement contribution. We re-derive in the strong coupling (diverging correlation length) regime, the logarithmic dependence of entanglement on the segment size predicted by conformal field theory for the boson universality class, and discuss its relation with the mode structure. We conjecture that the persistence of vacuum entanglement between arbitrarily separated finite size regions is connected with the localization of the highest frequency innermost modes.Comment: 23 pages, 19 figures, RevTex4. High resolution figures available upon request. New References adde

The difference between two random mixed quantum states: exact and asymptotic spectral analysis

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson's theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.Comment: 34 pages, 7 figures. Paper has been restructured with first section presenting all the results, with proofs in subsequent section

Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values

Classical-realistic analysis of entangled systems have lead to retrodiction paradoxes, which ordinarily have been dismissed on the grounds of counter-factuality. Instead, we claim that such paradoxes point to a deeper logical structure inherent to quantum mechanics, which is naturally described in the language of weak values, and which is accessible experimentally via weak measurements. Using as an illustration, a gedanken-experiment due to Hardy\cite{hardy}, we show that there is in fact an exact numerical coincidence between a) a pair of classically contradictory assertions about the locations of an electron and a positron, and b) the results of weak measurements of their location. The internal consistency of these results is due to the novel way by which quantum mechanics "resolves" the paradox: first, by allowing for two distinguishable manifestations of how the electron and positron can be at the same location: either as single particles or as a pair; and secondly, by allowing these properties to take either sign. In particular, we discuss the experimental meaning of a {\em negative} number of electron-positron pairs.Comment: 7 pages, 1 figur

Propuesta de proceso de contratación privada de mano de obra, en las empresas de construcción

Con este trabajo queremos proponer a las empresas del sector de la construcción, especialmente a las que se desenvuelven en el ámbito privado, un proceso documentado para la contratación de la mano de obra. En primer lugar, se revisarán algunos antecedentes sobre este tema, que es quizás uno de los aspectos que se maneja con mayor flexibilidad y sin el adecuado control en los proyectos de la construcción. En segundo lugar, revisaremos el marco legal de la contratación de la mano de obra, el tipo de relación entre las partes y las principales modalidades de contrato. Se revisará también el problema de la informalidad en la contratación y la ruta que se sigue para determinar un contratista, la competencia de la mano de obra, las unidades de medida, pago y precios, la liquidación, riesgos y garantías de los contratos. Basados en toda la fundamentación teórica mencionada, se justificará el porqué se debe estandarizar y controlar el proceso de contratación de la mano de obra, las ventajas de hacerlo y las características del proceso. Finalmente se presenta la propuesta del proceso de contratación de la mano de obra, explicando y mostrando en una gráfica y una tabla sus actividades principales, y la manera de desarrollar el mismo.We intend that the companies of the sector of the construction, especially those that are unwrapped into the private environment, a process documented for the recruiting of the manpower. In the first place some antecedents are revised on this topic that is maybe one of the aspects that is managed with more flexibility and without an appropriate control in the projects on construction. In second place the legal mark of the recruiting of the manpower, the relationship type between the parts and the main contract modalities is presented. It is also revised the problem of the informality in the recruiting and the route that it is continued to determine a contractor, the competition of the manpower, the measure units, payment and prices, the liquidation, the risks and guarantees of the contracts. Based on the whole mentioned theoretical foundation, it is justified the reason it should be standardized and to control the process of recruiting of the manpower, the advantages of making it and the characteristics of the process. Finally the proposal of the process on recruiting of the even manpower is presented the companies of the sector of construction, explaining and showing to them in a graph and a chart its main activities, and the way of developing the same one