Quantum Algorithms for Computing Maximal Quantum $f$-divergence and Kubo-Ando means

TL;DR

This paper introduces quantum algorithms for calculating maximal quantum $f$-divergences and Kubo-Ando means, unifying various quantum information measures within a single framework.

Contribution

It presents the first quantum algorithms for these quantities, leveraging Renyi entropies and matrix means to create a universal computational approach.

Findings

Algorithms efficiently compute quantum $f$-divergences.

Framework unifies multiple quantum information measures.

Potential applications in quantum information processing.

Abstract

The development of quantum computation has resulted in many quantum algorithms for a wide array of tasks. Recently, there is a growing interest in using quantum computing techniques to estimate or compute quantum information-theoretic quantities such as Renyi entropy, Von Neumann entropy, matrix means, etc. Motivated by these results, we present quantum algorithms for computing the maximal quantum $f$-divergences and the operator-theoretic matrix Kubo--Ando means. Both of them involve Renyi entropies, matrix means as special cases, thus implying the universality of our framework.