Nonparametric Learning Non-Gaussian Quantum States of Continuous Variable Systems.

Authors

Liubov Markovich, Xiaoyu Liu, Jordi Tura

Published in

Physical review letters. Volume 137. Issue 2. Pages 020201. Jul 10, 2026.

Abstract

Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum mechanics provides an accessible alternative by associating quantum states with classical probability distribution functions called tomograms. Despite its advantages, including compatibility with classical statistical methods, the tomographic method remains underutilized due to a lack of robust estimation techniques. This Letter addresses this gap by introducing a nonparametric kernel quantum state estimation (KQSE) framework for reconstructing quantum states and their trace characteristics from noisy data, without prior knowledge of the state. In contrast to existing methods, KQSE yields estimates of the density matrix in various bases, as well as trace quantities such as purity, higher moments, overlap, and trace distance, with a near-optimal convergence rate of O[over ˜](T^{-1}), where T is the total number of measurements. KQSE is robust for multimodal, non-Gaussian states, making it particularly well suited for characterizing states essential for quantum science.

PMID:
42503078
Bibliographic data and abstract were imported from PubMed on 26 Jul 2026.

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