One-shot quantum state exchange

Quantum state exchange is a quantum communication task in which two users exchange their respective quantum information in the asymptotic setting. In this paper, we consider a one-shot version of the quantum state exchange task, in which the users hold a single copy of the initial state, and they exchange their parts of the initial state by means of entanglement-assisted local operations and classical communication. We first derive lower bounds on the least amount of entanglement required for carrying out this task, and provide conditions on the initial state such that the protocol succeeds with zero entanglement cost. Based on these results, we study how the users deal with their symmetric information in order to reduce the entanglement cost. Moreover, we show that it is possible for the users to gain extra shared entanglement after this task.