An Efficient Alternating Minimization Algorithm for Computing Quantum Rate-Distortion Function

TL;DR

This paper introduces a new efficient alternating minimization algorithm for computing the quantum rate-distortion function, improving accuracy and efficiency over existing methods in quantum information theory.

Contribution

The paper presents an innovative algorithm that updates the Lagrangian multiplier iteratively and computes variables in closed form, avoiding complex nonlinear equations.

Findings

Algorithm demonstrates high accuracy in numerical experiments.

Significant efficiency improvements over previous methods.

Effectively solves the quantum rate-distortion problem without complex optimization.

Abstract

We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian analysis. Instead of fixing the multiplier corresponding to the distortion constraint, we update the multiplier in each iteration. Hence the algorithm solves the original problem itself, rather than the Lagrangian relaxation of it. Moreover, all the other variables are iterated in closed form without solving multi-dimensional nonlinear equations or multivariate optimization problems. Numerical experiments show the accuracy of our proposed algorithm and its improved efficiency over existing methods.