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arXiv · 2508.19085

Pretty Good Bounds on the worst-case Pretty Good Measurement

Sergio Escobar·Austin Pechan
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Abstract

We derive a new lower bound on the success probability of the Pretty Good Measurement (PGM) for worst-case quantum state discrimination among $m$ 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.

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Sergio Escobar, Austin Pechan. 2025-08-26. Pretty Good Bounds on the worst-case Pretty Good Measurement. https://arxiv.org/abs/2508.19085

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