Some characterizations for strong k-product states and strong k-locally broadcastable states based on mutual information

In multipartite composite quantum systems, nonproduct states and nonlocally broadcastable states are very important physical resources. In this paper, we first introduce the definition of strong k-product states, strong k-classical states, and strong k-locally broadcastable states; secondly, we propose the concept of the mutual information with respect to k-partition for multipartite quantum states, then define a correlation measure of nonstrong-k-product states based on the mutual information, and discuss some properties of this correlation measure. Finally, we obtain some equivalent and necessary conditions for strong k-locally broadcastable states based on mutual information.