Inseparability inequalities for higher-order moments for bipartite systems

There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context we study an example of a non-Gaussian state, which is a bipartite entangled state of the form $\psi(x_{\rm a},x_{\rm b})\propto (\alpha x_{\rm a}+\beta x_{\rm b})e^{-(x_{\rm a}^2+x_{\rm b}^2)/2}$. Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states.Comment: 7 pages, Submitte

Constraints for Three-Dimensional Higher-Spin Interactions and Conformal Correlators

In the context of higher-spin holography, we compare the classification of cubic interaction vertices for higher-spin gravity theories in three dimensions to the possible three-point correlation functions of conserved higher-spin currents in two-dimensional conformal field theories. In both cases, the allowed structures are governed by triangle inequalities for the involved spins. It is established that higher-order correlators satisfy similar polygon inequalities and that the same inequalities are valid for higher-order continuations of cubic vertices in the three-dimensional higher-spin gravity.Comment: 21 page

New Bell inequalities for the singlet state: Going beyond the Grothendieck bound

Contemporary versions of Bell's argument against local hidden variable (LHV) theories are based on the Clauser Horne Shimony and Holt (CHSH) inequality, and various attempts to generalize it. The amount of violation of these inequalities cannot exceed the bound set by the Grothendieck constants. However, if we go back to the original derivation by Bell, and use the perfect anti-correlation embodied in the singlet spin state, we can go beyond these bounds. In this paper we derive two-particle Bell inequalities for traceless two-outcome observables, whose violation in the singlet spin state go beyond the Grothendieck constants both for the two and three dimensional cases. Moreover, creating a higher dimensional analog of perfect correlations, and applying a recent result of Alon and his associates (Invent. Math. 163 499 (2006)) we prove that there are two-particle Bell inequalities for traceless two-outcome observables whose violation increases to infinity as the dimension and number of measurements grow. Technically these result are possible because perfect correlations (or anti-correlations) allow us to transport the indices of the inequality from the edges of a bipartite graph to those of the complete graph. Finally, it is shown how to apply these results to mixed Werner states, provided that the noise does not exceed 20%.Comment: 18 pages, two figures, some corrections and additional references, published versio

Health inequality in Nordic welfare states - more inequality or the wrong measures?

Several empirical papers have indicated that the health inequalities in the Nordic welfare states seem to be at least as high as health inequalities in other European countries even if the Nordic states have a more egalitarian income structure. This is in contrast to standard economic theory that predicts that income equality should lead to health equality everything else equal. We argue that there may be a straightforward explanation why Nordic countries appear to have a steeper health gradient than other countries. Health and income are related, and the correlation between income and health will be weaker the more noise there is in terms of other determinants of income. If the Nordic countries have succeeded in reducing the impacts of other determinants of income, like social class, then the correlation between income and health will be stronger in the Nordic countries. This story also holds for other measures of health inequality. However, if the causality is running from income to health, there may be a reason why health inequality is higher in more egalitarian states based on cognitive stress theory. We argue however, that even in this case the difference between Nordic states and the rest of Europe may be a result of poor measures.Health inequality; socio-economic status; Nordic welfare states; egalitarian countries

Leggett-Garg tests of macrorealism: checks for non-invasiveness and generalizations to higher-order correlators

In the tests for macrorealism proposed by Leggett and Garg, the temporal correlation functions of a dichotomic variable Q must be measured in a non-invasive way to rule out alternative classical explanations of Leggett-Garg inequality violations. Ideal negative measurements, in which a null result is argued to be a non-invasive determination of the system's state, are often used. From a quantum-mechanical perspective, such a measurement collapses the wave function and will therefore typically be found to be invasive under any experimental check. Here, a simple modified ideal negative measurement protocol is described for measuring the correlation functions which is argued to be non-invasive from both classical and quantum perspectives and hence the non-invasiveness can then be checked experimentally, thereby permitting a quantitative measure of the degree of clumsiness of the measurement. It is also shown how this procedure may be extended to measure higher-order correlation functions and a number of higher-order conditions for macrorealism are derived.Comment: 21 pages, Late