Unbounded violations of bipartite Bell Inequalities via Operator Space theory

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative $L_p$ embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise

Characterization of Extragalactic Point-Sources on E- and B-mode Maps of the CMB Polarization

Although interesting in themselves, extragalactic sources emitting in the microwave range (mainly radio-loud active galactic nuclei and dusty galaxies) are also considered a contaminant from the point of view of Cosmic Microwave Background (CMB) experiments. These sources appear as unresolved point-like objects in CMB measurements because of the limited resolution of CMB experiments. Amongst other issues, point-like sources are known to obstruct the reconstruction of the lensing potential, and can hinder the detection of the Primordial Gravitational Wave Background for low values of $r$. Therefore, extragalactic point-source detection and subtraction is a fundamental part of the component separation process necessary to achieve some of the science goals set for the next generation of CMB experiments. As a previous step to their removal, in this work we present a new filter based on steerable wavelets that allows the characterization of the emission of these extragalactic sources. Instead of the usual approach of working in polarization maps of the Stokes' $Q$ and $U$ parameters, the proposed filter operates on E- and B-mode polarization maps. In this way, it benefits from the lower intensity that, both, the CMB, and the galactic foreground emission, present in B-modes to improve its performance. To demonstrate its potential, we have applied the filter to simulations of the future PICO satellite, and we predict that, for the regions of fainter galactic foreground emission in the 30 GHz and 155 GHz bands of PICO, our filter will be able to characterize sources down to a minimum polarization intensity of, respectively, 125 pK and 14 pK. Adopting a $\Pi=0.02$ polarization degree, these values correspond to 169 mJy and 288 mJy intensities.Comment: 23 pages, 8 figures, accepted by JCA

Connes' embedding problem and Tsirelson's problem

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting C*-algebras. Connes' embedding problem asks whether any separable II$_1$ factor is a subfactor of the ultrapower of the hyperfinite II$_1$ factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positve answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

3D Motion Segmentation and 3D Localization of Mobile Robots Using an Array of Static Cameras and Objective Function Minimization

Abstract-This paper presents a method for obtaining the 3D motion segmentation and 3D localization of mobile robots using an array of calibrated cameras that are placed in fixed positions within the environment. This proposal does not rely on previous knowledge or invasive landmarks on board the robots. The proposal is based on the minimization of an objective function. This function includes information of all the cameras and depends on three groups of variables: the segmentation boundaries, the 3D rigid motion parameters (linear and angular velocity components) and depth (distance to the cameras). For the objective function minimization, we use a greedy algorithm that, after initialization, consists of three iterative steps. The use of multiple cameras increases notably the system robustness against occlusions and lighting changes. The accuracy of the results is also improved with regard to the methods where a single camera is used