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-ℓ1 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.
Authors:
- Nathaniel Johnston
- Benjamin Lovitz
- Jamie Sikora
- Vincent Russo
Download:
- Preprint from arXiv:2609.17411 [quant-ph]
Cite as:
- N. Johnston, B. Lovitz, V. Russo, and J. Sikora. Sharp bounds for perfect quantum state classification beyond antidistinguishability. E-print: arXiv:2609.17411 [quant-ph], 2026.