Operational Resource Theory of Non-Markovianity

Understand

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.