State transfer with quantum side information

TL;DR

This paper investigates quantum state transfer protocols with quantum side information, establishing optimal resource costs and providing operational interpretations for quantum mutual information and the chain rule.

Contribution

It introduces the concept of state transfer with quantum side information and determines the minimal non-local resources needed, offering new insights into quantum information measures.

Findings

Optimal resource costs for protocols are determined.

Quantum side information affects resource efficiency.

Provides operational meanings for quantum mutual information.

Abstract

We first consider quantum communication protocols between a sender Alice and a receiver Bob, which transfer Alice's quantum information to Bob by means of non-local resources, such as classical communication, quantum communication, and entanglement. In these protocols, we assume that Alice and Bob may have quantum side information, not transferred. In this work, these protocols are called the state transfer with quantum side information. We determine the optimal costs for non-local resources in the protocols, and study what the effects of the use of quantum side information are. Our results can give new operational meanings to the quantum mutual information and the quantum conditional mutual information, which directly provide us with an operational interpretation of the chain rule for the quantum mutual information.