The metric property of the quantum Jensen-Shannon divergence

In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The note proves that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, including the quantum state space.