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arXiv · 2506.11539

Completeness Stability of Quantum Measurements

Rakesh Saini·Jukka Kiukas·Daniel Burgarth·Alexei Gilchrist
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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.

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Rakesh Saini, Jukka Kiukas, Daniel Burgarth, Alexei Gilchrist. 2025-06-13. Completeness Stability of Quantum Measurements. https://doi.org/10.1103/wkj6-l7bf

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