Interior Point Methods for Structured Quantum Relative Entropy Optimization Problems

Understand

Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function.

• Recently, the self-concordance of a natural barrier function was proved for this set, and various implementations of interior-point methods have been made available to solve this class of optimization problems.
• In this paper, we show how common structures arising from applications in quantum information theory can be exploited to improve the efficiency of solving quantum relative entropy optimization problems using interior-point methods.
• First, we show that the natural barrier function for the epigraph of the quantum relative entropy composed with positive linear operators is self-concordant, even when these linear operators map to singular matrices.