Correlations in geometric states

Abstract: In this paper we explore the correlations in the geometric states. Here the geometric state means the state in CFTs that can be effectively described by classical geometry in the bulk in the semi-classical limit $G\to 0$. By using the upper bound of Holevo informaion we show the covex combination of geometric states cannot be a geometric state. To understand the duality between thermofield double state and eternal black hle, we construct several correlated states of two CFTs. In all the examples we show their correlations are too weak to produce the a connected spacetime. we review the measure named quantum discord and use it to characterize the classical and quantum correlations in quantum field theories. Finally, we discuss the correlations between two intervals $A$ and $B$ with distance $d$ in the vacuum state of 2D CFTs with large central charge $c$. The feature is the phase transition of the mutual information $I(\rho_{AB})$. We analyse the quasi-product state of $\rho_{AB}$ for large $d$. By using the Koashi-Winter relation of tripartite states the quantum and classical correlations between $A$ and $B$ can expressed as Holevo information, which provides a new understanding of the correlations as accessible information.