Learning Pure Quantum States in Any Dimension (Almost) Without Regret

ArXi:2605.09019v1 Announce Type: cross We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXi:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a rank-one projector for each copy using the previous outcomes, and performs the corresponding two-outcome projective measurement. The goal is to learn the state while keeping the chosen projectors close to the unknown state in order to minimize disturbance.