Sharp bounds for perfect quantum state classification beyond antidistinguishability

Abstract:A multiset of pure quantum states is said to be k-learnable if there is a measurement strategy that always narrows an unknown sample drawn from the list down to one of at most k candidates. The parameter k interpolates between distinguishability and antidistinguishability, and provides a unified framework for partial state identification. We prove two universal, and optimal, Gram-matrix criteria for k-learnability: a Frobenius-norm sufficient condition and an entrywise-$\ell_1$ necessary condition. We apply them to derive explicit learnability and copy-complexity guarantees for several well-known sets of states including SIC-POVMs, mutually unbiased bases, and stabilizer states. We further apply our results to zero-error mutation detection problems such as anomaly detection and changepoint detection.

32 pages. Comments welcome

arXiv:2609.17411 [quant-ph]

(or arXiv:2609.17411v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.17411 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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