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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.11539 |
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| _version_ | 1866912830695931904 |
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| author | Saini, Rakesh Kiukas, Jukka Burgarth, Daniel Gilchrist, Alexei |
| author_facet | Saini, Rakesh Kiukas, Jukka Burgarth, Daniel Gilchrist, Alexei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Completeness Stability of Quantum Measurements Saini, Rakesh Kiukas, Jukka Burgarth, Daniel Gilchrist, Alexei Quantum Physics 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. |
| title | Completeness Stability of Quantum Measurements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.11539 |