QLunch: Markovianizing cost of tripartite quantum states

Speaker: Eyuri Wakakuwa; University of Tokyo, Japan

Title: Markovianizing cost of tripartite quantum states

We introduce a task that we call Markovianization, in which a tripartite quantum state is transformed to an approximate quantum Markov chain by a random unitary operation on one of the three subsystems. We consider an asymptotic limit of infinite copies and vanishingly small error, and define the Markovianizing cost as the minimum cost of randomness per copy required for the task. We derive a single-letter formula for the Markovianizing cost of pure states based on the Koashi-Imoto decomposition, and prove that it can be computed by a finite-step algorithm. The result have an application in an analysis of entanglement-assisted LOCC implementations of bipartite unitary gates.