Completeness Stability of Quantum Measurements

• URL: http://arxiv.org/abs/2506.11539v1
• Date: Fri, 13 Jun 2025 07:44:53 GMT
• Title: Completeness Stability of Quantum Measurements
• Authors: Rakesh Saini, Jukka Kiukas, Daniel Burgarth, Alexei Gilchrist,
• Abstract summary: We introduce a resource monotone, the completeness stability, to quantify the quality of quantum measurements.<n>By viewing a quantum measurement as a frame, the minimum eigenvalue of a frame operator emerges as a significant monotone.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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