Learning pure quantum states (almost) without regret
- URL: http://arxiv.org/abs/2406.18370v2
- Date: Thu, 05 Jun 2025 10:09:29 GMT
- Title: Learning pure quantum states (almost) without regret
- Authors: Josep Lumbreras, Mikhail Terekhov, Marco Tomamichel,
- Abstract summary: We study the study of sample-optimal quantum state tomography with minimal disturbance to the samples.<n>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?
- Score: 7.988085110283119
- License: http://creativecommons.org/licenses/by/4.0/
- 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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