Measurement dependent locality

The demonstration and use of Bell-nonlocality, a concept that is fundamentally striking and is at the core of applications in device independent quantum information processing, relies heavily on the assumption of measurement independence, also called the assumption of free choice. The latter cannot be verified or guaranteed. In this paper, we consider a relaxation of the measurement independence assumption. We briefly review the results of Phys. Rev. Lett. 113, 190402 (2014), which show that with our relaxation, the set of so-called measurement dependent local (MDL) correlations is a polytope, i.e. it can be fully described using a finite set of linear inequalities. Here we analyze this polytope, first in the simplest case of 2 parties with binary inputs and outputs, for which we give a full characterization. We show that partially entangled states are preferable to the maximally entangled state when dealing with measurement dependence in this scenario. We further present a method which transforms any Bell-inequality into an MDL inequality and give valid inequalities for the case of arbitrary number of parties as well as one for arbitrary number of inputs. We introduce the assumption of independent sources in the measurement dependence scenario and give a full analysis for the bipartite scenario with binary inputs and outputs. Finally, we establish a link between measurement dependence and another strong hindrance in certifying nonlocal correlations: nondetection events.Comment: 16+7 pages, 2 figure

Upper Bounds on the Rate of Low Density Stabilizer Codes for the Quantum Erasure Channel

Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is below 1-2p, for stabilizer codes: we also derive an improved upper bound of the form : R is below 1-2p-D(p) with a function D(p) that stays positive for 0 < p < 1/2 and for any family of stabilizer codes whose generators have weights bounded from above by a constant - low density stabilizer codes. We obtain an application to percolation theory for a family of self-dual tilings of the hyperbolic plane. We associate a family of low density stabilizer codes with appropriate finite quotients of these tilings. We then relate the probability of percolation to the probability of a decoding error for these codes on the quantum erasure channel. The application of our upper bound on achievable rates of low density stabilizer codes gives rise to an upper bound on the critical probability for these tilings.Comment: 32 page

Asymptotic Preserving numerical schemes for multiscale parabolic problems

We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\varepsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently the asymptotic behaviour as $\varepsilon \rightarrow 0$, without using a dramatically fine spatial discretization at the scale of the fast oscillations. However, known such homogenization schemes are in general not accurate for both the highly oscillatory regime $\varepsilon \rightarrow 0$ and the non oscillatory regime $\varepsilon \sim 1$. In this paper, we introduce an Asymptotic Preserving method based on an exact micro-macro decomposition of the solution which remains consistent for both regimes.Comment: 7 pages, to appear in C. R. Acad. Sci. Paris; Ser.

A Construction of Quantum LDPC Codes from Cayley Graphs

We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi. It is based on the Cayley graph of Fn together with a set of generators regarded as the columns of the parity-check matrix of a classical code. We give a general lower bound on the minimum distance of the Quantum code in $\mathcal{O}(dn^2)$ where d is the minimum distance of the classical code. When the classical code is the $[n, 1, n]$ repetition code, we are able to compute the exact parameters of the associated Quantum code which are $[[2^n, 2^{\frac{n+1}{2}}, 2^{\frac{n-1}{2}}]]$.Comment: The material in this paper was presented in part at ISIT 2011. This article is published in IEEE Transactions on Information Theory. We point out that the second step of the proof of Proposition VI.2 in the published version (Proposition 25 in the present version and Proposition 18 in the ISIT extended abstract) is not strictly correct. This issue is addressed in the present versio

Intensity Correlation between Observations at Differrent Wavelengths for Mkn 501 in 1997

The CAT imaging telescope on the site of the former solar plant Th'emis in southern France observed gamma-rays from the BL Lac object Mkn501 above 250 GeV for more than 60 usable hours on-source from March to October 1997. This source was in a state of high activity during all this period. By studying the correlation between the photons of different energies detected by the CAT imaging telescope and by the ASM/RXTE experiment (1.3-12.0 keV) on board the Rossi X-Ray Timing Explorer, we may constrain the mechanisms which could lead to the emission of these photons.Comment: Proceedings of the 19th Texas Symposium. 8 pages, 7 figure

Cache policies for cloud-based systems: To keep or not to keep

In this paper, we study cache policies for cloud-based caching. Cloud-based caching uses cloud storage services such as Amazon S3 as a cache for data items that would have been recomputed otherwise. Cloud-based caching departs from classical caching: cloud resources are potentially infinite and only paid when used, while classical caching relies on a fixed storage capacity and its main monetary cost comes from the initial investment. To deal with this new context, we design and evaluate a new caching policy that minimizes the overall cost of a cloud-based system. The policy takes into account the frequency of consumption of an item and the cloud cost model. We show that this policy is easier to operate, that it scales with the demand and that it outperforms classical policies managing a fixed capacity.Comment: Proceedings of IEEE International Conference on Cloud Computing 2014 (CLOUD 14

Compressive Spectral Clustering

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features to separate objects into k classes. Each of these three steps becomes computationally intensive for large N and/or k. We propose to speed up the last two steps based on recent results in the emerging field of graph signal processing: graph filtering of random signals, and random sampling of bandlimited graph signals. We prove that our method, with a gain in computation time that can reach several orders of magnitude, is in fact an approximation of spectral clustering, for which we are able to control the error. We test the performance of our method on artificial and real-world network data.Comment: 12 pages, 2 figure

Deformable Part-based Fully Convolutional Network for Object Detection

Existing region-based object detectors are limited to regions with fixed box geometry to represent objects, even if those are highly non-rectangular. In this paper we introduce DP-FCN, a deep model for object detection which explicitly adapts to shapes of objects with deformable parts. Without additional annotations, it learns to focus on discriminative elements and to align them, and simultaneously brings more invariance for classification and geometric information to refine localization. DP-FCN is composed of three main modules: a Fully Convolutional Network to efficiently maintain spatial resolution, a deformable part-based RoI pooling layer to optimize positions of parts and build invariance, and a deformation-aware localization module explicitly exploiting displacements of parts to improve accuracy of bounding box regression. We experimentally validate our model and show significant gains. DP-FCN achieves state-of-the-art performances of 83.1% and 80.9% on PASCAL VOC 2007 and 2012 with VOC data only.Comment: Accepted to BMVC 2017 (oral