15
1

Sample-optimal learning of quantum states using gentle measurements

Main:35 Pages
1 Figures
Bibliography:5 Pages
Abstract

Gentle measurements of quantum states do not entirely collapse the initial state. Instead, they provide a post-measurement state at a prescribed trace distance α\alpha from the initial state together with a random variable used for quantum learning of the initial state. We introduce here the class of α\alpha-locally-gentle measurements (α\alpha-LGM) on a finite dimensional quantum system which are product measurements on product states and prove a strong quantum Data-Processing Inequality (qDPI) on this class using an improved relation between gentleness and quantum differential privacy. We further show a gentle quantum Neyman-Pearson lemma which implies that our qDPI is asymptotically optimal (for small α\alpha). This inequality is employed to show that the necessary number of quantum states for prescribed accuracy ϵ\epsilon is of order 1/(ϵ2α2)1/(\epsilon^2 \alpha^2) for both quantum tomography and quantum state certification. Finally, we propose an α\alpha-LGM called quantum Label Switch that attains these bounds. It is a general implementable method to turn any two-outcome measurement into an α\alpha-LGM.

View on arXiv
@article{butucea2025_2505.24587,
  title={ Sample-optimal learning of quantum states using gentle measurements },
  author={ Cristina Butucea and Jan Johannes and Henning Stein },
  journal={arXiv preprint arXiv:2505.24587},
  year={ 2025 }
}
Comments on this paper

We use cookies and other tracking technologies to improve your browsing experience on our website, to show you personalized content and targeted ads, to analyze our website traffic, and to understand where our visitors are coming from. See our policy.