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-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.
Related
- The Filtering Demon: Beyond Standard Thermodynamic Bounds and Harnessing Measurement Error and Quantum Friction
- Quantum Barankin bounds beyond local unbiasedness: Analytic results for Gaussian states via a right-division framework
- A complete classification of perfect state transfer in Grover walks on abelian Cayley graphs
- Antidistinguishability of states in General Probabilistic Theories
- Post-Quantum Perfect Zero-Knowledge Arguments for NP From Any One-Way Permutation
BibTeX
@misc{johnston2026sharp,
title = {{Sharp bounds for perfect quantum state classification beyond antidistinguishability}},
author = {Nathaniel Johnston and Benjamin Lovitz and Vincent Russo and Jamie Sikora},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17411},
eprint = {2609.17411},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17411},
}
RIS
TY - UNPB
TI - Sharp bounds for perfect quantum state classification beyond antidistinguishability
AU - Nathaniel Johnston
AU - Benjamin Lovitz
AU - Vincent Russo
AU - Jamie Sikora
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17411
UR - https://arxiv.org/abs/2609.17411
AB - 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-ℓ_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.
ER -