It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

CuCo 2 O 4 and CuO?Co 3 O 4 compounds were prepared by a one-pot simple molten salt method (MSM) at 280 uC to 750 uC. Changes in morphology, crystal structure and electrochemical properties of CuCo 2 O 4 as a function of preparation temperatures were investigated using X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and Brunauer-Emmett-Teller absorption isotherm. XRD patterns of the sample prepared at 280 uC show a crystalline cubic structure with a lattice parameter value of a = 8.131 A ˚and a surface area value of 9.8 m 2 g 21 . The sample prepared at temperatures .510 uC shows the presence of CuO?Co 3 O 4 phases. Energy storage properties are evaluated using cyclic voltammetry (CV) and galvanostatic cycling studies. CV studies show a main anodic peak at y2.1 V and cathodic peak at y1.2 V. At a current rate of 60 mA g 21 and in the voltage range of 0.005-3.0 V vs. Li, CuCo 2 O 4 composite prepared at 510 uC shows a high and stable capacity of y680 (quenched) and 740 (slow cooling) mAh g 21 at the end of the 40th cycle.

The possibility of Bell inequality violations in quantum theory had a profound impact on our understanding of the correlations that can be shared by distant parties. Generalizing the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is, however, challenging. Here, we investigate constraints on correlations in networks under the natural assumptions of no-signaling and independence of the sources. We consider the triangle network with binary outputs, and derive strong constraints on correlations even though the parties receive no input, i.e., each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network with binary outputs.

No abstract