Pretty Good Bounds on the worst-case Pretty Good Measurement

• URL: http://arxiv.org/abs/2508.19085v3
• Date: Thu, 09 Oct 2025 17:50:52 GMT
• Title: Pretty Good Bounds on the worst-case Pretty Good Measurement
• Abstract summary: We derive a new lower bound on the success probability of the Pretty Good Measurement for worst-case quantum state discrimination.<n>Our bound is strictly tighter than the previously known Gram-matrix-based bound for $mgeq 4$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive a new lower bound on the success probability of the Pretty Good Measurement (PGM) for worst-case quantum state discrimination among $m$ quantum 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.

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