Local and nonlocal content of bipartite qubit and qutrit correlations

Abstract

The local and nonlocal contents of nonlocal probability distributions are studied using the approach of Elitzur, Popescu, and Rohrlich [A. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A 162, 25 (1992)]. This work focuses on distributions that can be obtained by single-copy von Neumann measurements on bipartite quantum systems. For pure two-qubit states $|\ensuremath{\Psi}(\ensuremath{\theta})⟩=\text{cos}\text{ }\ensuremath{\theta}|00⟩+\text{sin}\text{ }\ensuremath{\theta}|11⟩$ (with $\text{cos}\text{ }\ensuremath{\theta}\ensuremath{\ge}\text{sin}\text{ }\ensuremath{\theta}$), the local content of the corresponding probability distribution is found to lie between $1\ensuremath{-}\text{sin}\text{ }2\ensuremath{\theta}$ and $\text{cos}\text{ }2\ensuremath{\theta}$. For the family $|\ensuremath{\Psi}(\ensuremath{\gamma})⟩=(|00⟩+|11⟩+\ensuremath{\gamma}|22⟩)/\sqrt{2+{\ensuremath{\gamma}}^{2}}$ of two-qutrit states, nonzero local content is found for $\ensuremath{\gamma}>2$.