State exchange with quantum side information

TL;DR

This paper investigates the quantum state exchange task with quantum side information, deriving bounds on entanglement cost and revealing scenarios where the cost can be negative, thus advancing quantum communication theory.

Contribution

It provides the first bounds on entanglement cost for state exchange with quantum side information and characterizes conditions for optimal entanglement use.

Findings

Optimal entanglement cost can be negative with quantum side information.

Derived general upper and lower bounds for entanglement requirements.

Identified conditions for exact optimal entanglement cost.

Abstract

We consider a quantum communication task between two users Alice and Bob, in which Alice and Bob exchange their respective quantum information by means of local operations and classical communication assisted by shared entanglement. Here, we assume that Alice and Bob may have quantum side information, not transferred, and classical communication is free. In this work, we derive general upper and lower bounds for the least amount of entanglement which is necessary to perfectly perform this task, called the state exchange with quantum side information. Moreover, we show that the optimal entanglement cost can be negative when Alice and Bob make use of their quantum side information. We finally provide conditions on the initial state for the state exchange with quantum side information which give the exact optimal entanglement cost.