Concentrating tripartite quantum information

TL;DR

This paper introduces the concept of concentrated information in tripartite quantum states, providing bounds, exact expressions for certain states, and exploring its role in quantum state merging and related informational tasks.

Contribution

It defines and analyzes the concentrated information measure, linking it to entanglement, discord, and state merging, and provides new bounds and exact formulas for various states.

Findings

Concentrated information unifies several quantum informational quantities.

Bounds and formulas for concentrated information are derived for specific classes of states.

Classical communication can enhance mixed state merging, unlike pure states.

Abstract

We introduce the concentrated information of tripartite quantum states. For three parties Alice, Bob, and Charlie, it is defined as the maximal mutual information achievable between Alice and Charlie via local operations and classical communication performed by Charlie and Bob. We derive upper and lower bounds to the concentrated information, and obtain a closed expression for it on several classes of states including arbitrary pure tripartite states in the asymptotic setting. We show that distillable entanglement, entanglement of assistance, and quantum discord can all be expressed in terms of the concentrated information, thus revealing its role as a unifying informational primitive. We finally investigate quantum state merging of mixed states with and without additional entanglement. The gap between classical and quantum concentrated information is proven to be an operational figure of merit for mixed state merging in absence of additional entanglement. Contrary to pure state merging, our analysis shows that classical communication in both directions can provide advantage for merging of mixed states.