Testing microscopic discretization

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate gaussian distributions can be approximated by sums of finitely-valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra.Comment: Proof of strong NP-hardness. Connection with random walks. New asymptotic results. Numerous typos correcte

Reconstruction Algorithms for Sums of Affine Powers

In this paper we study sums of powers of affine functions in (mostly) one variable. Although quite simple, this model is a generalization of two well-studied models: Waring decomposition and sparsest shift. For these three models there are natural extensions to several variables, but this paper is mostly focused on univariate polynomials. We present structural results which compare the expressive power of the three models; and we propose algorithms that find the smallest decomposition of f in the first model (sums of affine powers) for an input polynomial f given in dense representation. We also begin a study of the multivariate case. This work could be extended in several directions. In particular, just as for Sparsest Shift and Waring decomposition, one could consider extensions to "supersparse" polynomials and attempt a fuller study of the multi-variate case. We also point out that the basic univariate problem studied in the present paper is far from completely solved: our algorithms all rely on some assumptions for the exponents in an optimal decomposition, and some algorithms also rely on a distinctness assumption for the shifts. It would be very interesting to weaken these assumptions, or even to remove them entirely. Another related and poorly understood issue is that of the bit size of the constants appearing in an optimal decomposition: is it always polynomially related to the bit size of the input polynomial given in dense representation?Comment: This version improves on several algorithmic result

Técnica, posthumanismo, experiencia

El presente trabajo propone una reflexión sobre la técnica y sobre las condiciones de una crítica de la técnica en el horizonte contemporáneo del agotamiento de los paradigmas humanistas desde los que tradicionalmente se pensó esa crítica. Se plantea que la pregunta por la técnica ha de diferenciarse de la pregunta (instrumental) por los dispositivos técnicos, es decir, ha de partir de la ruptura con el supuesto humanista de la exterioridad entre técnica y humanidad. Una vez planteada esta escena posthumanista se proponen distintas alternativas posibles en ese horizonte, que oscilan entre el cinismo antropotécnico y el experimentalismo radical postidentitario. Finalmente, el trabajo postula que la puesta en disposición del lenguaje (en tanto transparencia) y de la temporalidad (en cuanto velocidad) son los parámetros clave del contemporáneo capitalismo de la información. Ante ello, se propone que el desafío fundamental de un posthumanismo radical es abrir una experiencia del lenguaje y del tiempo más allá de toda forma de disponibilidad.Fil: Garcia Garcia, Luis Ignacio. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Centro de Investigaciones María Saleme Burnichón; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Irreversibility in quantum maps with decoherence

The Bolztmann echo (BE) is a measure of irreversibility and sensitivity to perturbations for non-isolated systems. Recently, different regimes of this quantity were described for chaotic systems. There is a perturbative regime where the BE decays with a rate given by the sum of a term depending on the accuracy with which the system is time-reversed and a term depending on the coupling between the system and the environment. In addition, a parameter independent regime, characterised by the classical Lyapunov exponent, is expected. In this paper we study the behaviour of the BE in hyperbolic maps that are in contact with different environments. We analyse the emergence of the different regimes and show that the behaviour of the decay rate of the BE is strongly dependent on the type of environment.Comment: 13 pages, 3 figures