Learning Pure Quantum States in Any Dimension (Almost) Without Regret
We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv: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. The qubit solution relies on the special geometry of the Bloch sphere and does not extend directly to qudits, where pure states form a curved manifold. We show that this obstruction can be overcome by...
| Authors | Josep Lumbreras, Marco Tomamichel |
|---|---|
| Primary category | quant-ph |
| Published | 9 May 2026 |
| Last updated at source | 9 May 2026 |
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