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arXiv · 2406.18370

Learning pure quantum states (almost) without regret

Josep Lumbreras·Mikhail Terekhov·Marco Tomamichel
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Abstract

We initiate the study of sample-optimal quantum state tomography with minimal disturbance to the samples. Can we efficiently learn a precise description of a quantum state through sequential measurements of samples while at the same time making sure that the post-measurement state of the samples is only minimally perturbed? Defining regret as the cumulative disturbance of all samples, the challenge is to find a balance between the most informative sequence of measurements on the one hand and measurements incurring minimal regret on the other. Here we answer this question for qubit states by exhibiting a protocol that for pure states achieves maximal precision while incurring a regret that grows only polylogarithmically with the number of samples, a scaling that we show to be optimal.

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Josep Lumbreras, Mikhail Terekhov, Marco Tomamichel. 2024-06-26. Learning pure quantum states (almost) without regret. https://arxiv.org/abs/2406.18370

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