Pretty Good Bounds on the worst-case Pretty Good Measurement
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912928311017472 |
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| author | Escobar, Sergio Pechan, Austin |
| author_facet | Escobar, Sergio Pechan, Austin |
| contents | We derive a new lower bound on the success probability of the Pretty Good Measurement (PGM) for worst-case quantum state discrimination among $m$ pure states. Our bound is strictly tighter than the previously known Gram-matrix-based bound for $m\geq 4$. The proof adapts techniques from Barnum and Knill's analysis of the average-case PGM, applied here to the worst-case scenario. By comparing the PGM to the sequential measurement algorithm, we obtain a guarantee showing that, in the low-fidelity regime, the PGM's success probability decreases quadratically with respect to the maximum pairwise overlap, rather than linearly as in earlier bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pretty Good Bounds on the worst-case Pretty Good Measurement Escobar, Sergio Pechan, Austin Quantum Physics We derive a new lower bound on the success probability of the Pretty Good Measurement (PGM) for worst-case quantum state discrimination among $m$ pure states. Our bound is strictly tighter than the previously known Gram-matrix-based bound for $m\geq 4$. The proof adapts techniques from Barnum and Knill's analysis of the average-case PGM, applied here to the worst-case scenario. By comparing the PGM to the sequential measurement algorithm, we obtain a guarantee showing that, in the low-fidelity regime, the PGM's success probability decreases quadratically with respect to the maximum pairwise overlap, rather than linearly as in earlier bounds. |
| title | Pretty Good Bounds on the worst-case Pretty Good Measurement |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.19085 |