Reliable optimization of arbitrary functions over quantum measurements

TL;DR

This paper introduces reliable algorithms that combine Gilbert's convex optimization method with gradient techniques to optimize arbitrary functions over quantum measurements, applicable to tasks like quantum tomography and channel capacity calculation.

Contribution

The paper presents a novel algorithmic framework for optimizing any function over quantum measurements, integrating Gilbert's algorithm with gradient methods for improved reliability.

Findings

Algorithms work effectively on convex functions.

Algorithms also perform well on nonconvex functions.

Demonstrated applications in quantum tomography and channel capacity.

Abstract

As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often considered as a basic yet important problem in various applications. Typical examples include but not limited to optimizing the likelihood functions in quantum measurement tomography, searching the Bell parameters in Bell-test experiments, and calculating the capacities of quantum channels. In this work, we propose reliable algorithms for optimizing arbitrary functions over the space of quantum measurements by combining the so-called Gilbert's algorithm for convex optimization with certain gradient algorithms. With extensive applications, we demonstrate the efficacy of our algorithms with both convex and nonconvex functions.