Identifying an unknown quantum state is one of the oldest and most fundamental problems in quantum information theory. In this talk, we examine a variant of this problem—quantum state classification—in which the learner is allowed multiple guesses, provided that one of them must be correct. A collection of quantum states is said to be k-learnable if the correct state can always be identified with at most k guesses and zero error. We present examples illustrating when perfect classification is possible, derive optimal bounds for various values of k, and characterize the computational complexity of deciding k-learnability.

This is joint work with Vincent Russo, Nathaniel Johnston, and Benjamin Lovitz (arXiv: 2510.20789, 2311.17047, 2206.08313).

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