Reliable Optimization of Arbitrary Functions over Quantum Measurements

Jing Luo, Jiangwei Shang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 are 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.

Original languageEnglish
Article number358
JournalEntropy
Volume25
Issue number2
DOIs
Publication statusPublished - Feb 2023

Keywords

  • Gilbert’s algorithm
  • convex optimization
  • nonconvex optimization
  • quantum measurement

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