  We first consider quantum communication protocols between a sender Alice and
a receiver Bob, which transfer Alice's quantum information to Bob by means of
non-local resources, such as classical communication, quantum communication,
and entanglement. In these protocols, we assume that Alice and Bob may have
quantum side information, not transferred. In this work, these protocols are
called the state transfer with quantum side information. We determine the
optimal costs for non-local resources in the protocols, and study what the
effects of the use of quantum side information are. Our results can give new
operational meanings to the quantum mutual information and the quantum
conditional mutual information, which directly provide us with an operational
interpretation of the chain rule for the quantum mutual information.
