Seminar at SMU Delhi
August 7, 2013 (Wednesday) ,
3:30 PM at Webinar
Indian Statistical Institute, Bangalore
Covariance Realization Problem for Spin Systems
Abstract of Talk
In this talk, I will discuss the necessary and sufficient conditions for the realizability of a correlation matrix of order $n \geq 2$ as a correlation matrix of a vector of spin random variables. Deriving the form of the optimal solution of a maximum entropy problem, we obtain an infinite family of linear inequalities characterizing the polytope of spin correlation matrices. We shall see that for $n \leq 6$ the facet description of such polytope is provided through a minimal system of Bell-type inequalities.
Finally, I will talk about some explicit methods to determine the maximum entropy measure that realizes a given matrix $C$ as a spin correlation matrix, provided that $C$ is realizable.