Search Results (4)

For any experiment with two entangled photons, some joint measurement outcomes can have zero probability for a precise choice of basis. These perfect anti-correlations would seem to be a purely quantum phenomenon. It is, therefore, surprising that these very anti-correlations are also evident when the input to the same experiment is analyzed via classical electromagnetic theory. Demonstrating this quantum–classical connection for arbitrary two-photon states and analyzing why it is successful motivates alternative perspectives concerning entanglement, the path integral, and other topics in quantum foundations. Full article

ESG ratings are data-driven indices, focused on three key pillars (Environmental, Social, and Governance), which are used by investors in order to evaluate companies and countries, in terms of Sustainability. A reasonable question which arises is how these ratings are associated to each other. The research purpose of this work is to provide the first analysis of correlation networks, constructed from ESG ratings of selected economies. The networks are constructed based on Pearson correlation and analyzed in terms of some well-known tools from Network Science, namely: degree centrality of the nodes, degree centralization of the network, network density and network balance. We found that the Prevalence of Overweight and Life Expectancy are the most central ESG ratings, while unexpectedly, two of the most commonly used economic indicators, namely the GDP growth and Unemployment, are at the bottom of the list. China’s ESG network has remarkably high positive and high negative centralization, which has strong implications on network’s vulnerability and targeted controllability. Interestingly, if the sign of correlations is omitted, the above result cannot be captured. This is a clear example of why signed network analysis is needed. The most striking result of our analysis is that the ESG networks are extremely balanced, i.e. they are split into two anti-correlated groups of ESG ratings (nodes). It is impressive that USA’s network achieves 97.9% balance, i.e. almost perfect structural split into two anti-correlated groups of nodes. This split of network structure may have strong implications on hedging risk, if we see ESG ratings as underlying assets for portfolio selection. Investing into anti-correlated assets, called as "hedge assets", can be useful to offset potential losses. Our future direction is to apply and extend the proposed signed network analysis to ESG ratings of corporate organizations, aiming to design optimal portfolios with desired balance between risk and return. Full article

The famous singlet correlations of a composite quantum system consisting of two two-level components in the singlet state exhibit notable features of two kinds. One kind are striking certainty relations: perfect anti-correlation, and perfect correlation, under certain joint settings. The other kind are a number of symmetries, namely invariance under a common rotation of the settings, invariance under exchange of components, and invariance under exchange of both measurement outcomes. One might like to restrict attention to rotations in the plane since those are the ones most commonly investigated experimentally. One can then also further distinguish between the case of discrete rotations (e.g., only settings which are a whole number of degrees are allowed) and continuous rotations. We study the class of classical correlation functions, i.e., generated by classical physical systems, satisfying all these symmetries, in the continuous, planar, case. We call such correlation functions classical EPR-B correlations. It turns out that if the certainty relations and rotational symmetry holds at the level of the correlations, then rotational symmetry can be imposed “for free” on the underlying classical physical model by adding an extra randomisation level. The other binary symmetries are obtained “for free”. This leads to a simple heuristic description of all possible classical EPR-B correlations in terms of a “spinning bi-coloured disk” model. We deliberately use the word “heuristic” because technical mathematical problems remain wide open concerning the transition from finite or discrete to continuous. The main purpose of this paper is to bring this situation to the attention of the mathematical community. We do show that the widespread idea that “quantum correlations are more extreme than classical physics would allow” is at best highly inaccurate, through giving a concrete example of a classical correlation which satisfies all the symmetries and all the certainty relations and which exceeds the quantum correlations over a whole range of settings. It is found by a search procedure in which we randomly generate classical physical models and, for each generated model, evaluate its properties in a further Monte-Carlo simulation of the model itself. Full article

We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by $\frac{3}{2}$ and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound $\frac{3}{2}$ for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study. Full article