Revealing Tripartite Quantum Discord with Tripartite Information Diagram

A new measure based on the tripartite information diagram is proposed for identifying quantum discord in tripartite systems. The proposed measure generalizes the mutual information underlying discord from bipartite to tripartite systems, and utilizes both one-particle and two-particle projective measurements to reveal the characteristics of the tripartite quantum discord. The feasibility of the proposed measure is demonstrated by evaluating the tripartite quantum discord for systems with states close to Greenberger-Horne-Zeilinger, W, and biseparable states. In addition, the connections between tripartite quantum discord and two other quantum correlations---namely genuine tripartite entanglement and genuine tripartite Einstein-Podolsky-Rosen steering---are briefly discussed. The present study considers the case of quantum discord in tripartite systems. However, the proposed framework can be readily extended to general N-partite systems

A Generalized Jarque-Bera Test of Conditional Normality

We consider testing normality in a general class of models that admits nonlinear conditional mean and conditional variance functions. We derive the asymptotic distribution of the skewness and kurtosis coefficients of the model’s standardized residuals and propose an asymptotic x2 test of normality. This test simplifies to the Jarque-Bera test only when: (i) the conditional mean function contains an intercept term but does not depend on past errors, and (ii) the errors are conditionally homoskedastic. Beyond this context, it is shown that the Jarque-Bera test has size distortion but the proposed test does not.conditional heteroskedsaticity, conditional normality, Jarque-Bera test