Semidefinite optimization of the quantum relative entropy of channels
It solves the computational problem of maximizing quantum relative entropy for channels, which is important for quantum information theory and resource theories.
The paper introduces a method to compute the quantum relative entropy of channels, providing upper and lower bounds that converge to the true value with arbitrary precision. This enables practical computation for channel discrimination and resource theories.
This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the optimization of relative entropy for quantum states [Koßmann and Schwonnek, arXiv:2404.17016], we introduce a discretized linearization of the integral representation for the relative entropy of states, enabling us to handle maximization tasks for the relative entropy of channels. Our approach here extends previous work on minimizing relative entropy to the more complicated domain of maximization. It also provides efficiently computable upper and lower bounds that sandwich the true value with any desired precision, leading to a practical method for computing the relative entropy of channels.