Completeness Stability of Quantum Measurements
Abstract
We introduce a resource monotone, the completeness stability, to quantify the quality of quantum measurements within a resource-theoretic framework. By viewing a quantum measurement as a frame, the minimum eigenvalue of a frame operator emerges as a significant monotone. It captures bounds on estimation errors and the numerical stability of inverting the frame operator to calculate the optimal dual for state reconstruction. Maximizing this monotone identifies a well-characterized class of quantum measurements forming weighted complex projective 2-designs, which includes well-known examples such as SIC-POVMs. Our results provide a principled framework for comparing and optimizing quantum measurements for practical applications.
Cite
@article{arxiv.2506.11539,
title = {Completeness Stability of Quantum Measurements},
author = {Rakesh Saini and Jukka Kiukas and Daniel Burgarth and Alexei Gilchrist},
journal= {arXiv preprint arXiv:2506.11539},
year = {2026}
}
Comments
11 pages, 2 figures