  In order to analyze non-Markovianity of tripartite quantum states from a
resource theoretical viewpoint, we introduce a class of quantum operations
performed by three distant parties, and investigate an operational resource
theory (ORT) induced it. A tripartite state is a free state if and only if it
is a quantum Markov chain. We prove monotonicity of functions such as the
conditional quantum mutual information, intrinsic information, squashed
entanglement, a generalization of entanglement of purification, and the
relative entropy of recovery. The ORT has five bound sets, each of which
corresponds to one of the monotone functions. We introduce a task of
"non-Markovianity dilution", and prove that the optimal rate for the task,
namely the "non-Markovianity cost", is bounded from above by entanglement of
purification in the case of pure states. We also propose a classical resource
theory of non-Markovianity.
