Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach

Understand

To quantify non-Markovianity of tripartite quantum states from an operational viewpoint, we introduce a class $\Omega^*$ of operations performed by three distant parties.

• A tripartite quantum state is a free state under $\Omega^*$ if and only if it is a quantum Markov chain.
• We introduce a function of tripartite quantum states that we call the non-Markovianity of formation, and prove that it is a faithful measure of non-Markovianity, which is continuous and monotonically nonincreasing under a subclass $\Omega$ of $\Omega^*$.
• We consider a task in which the three parties generate a non-Markov state from scratch by operations in $\Omega$, assisted with quantum communication from the third party to the others, which does not belong to $\Omega$.