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Quantum learning theory with continuous-variable systems
This talk investigates the intersection between two important fields of quantum information: quantum learning theory and continuous-variable (CV) systems. Quantum learning theory addresses the question of how to extract classical information from quantum systems as efficiently as possible. CV systems are ubiquitous in nature and in quantum technologies, as they model bosonic systems and quantum optical platforms. The intersection between these two fields raises many interesting open questions, some of which are addressed in our recent works. The first natural question is: what are the ultimate achievable performances of tomography for CV systems? In [Nature Physics volume 21, pages 2002–2008 (2025)], we answer this question by proving that: (i) tomography of non-Gaussian states is extremely inefficient; (ii) tomography of Gaussian states is efficient; and (iii) the sample complexity of CV tomography grows exponentially with the degree of non-Gaussianity of the unknown state. Other natural questions explored in our recent works include: How can we efficiently learn Gaussian processes? And how can we efficiently test whether an unknown CV state is Gaussian or far from the set of Gaussian states? As a by-product of our analysis, we establish several bounds on the trace distance between CV states in terms of their covariance matrices, which may be of independent interest. This talk will be a summary of the main results of our recent papers on quantum learning theory with CV systems:
Nature Physics volume 21, pages 2002–2008 (2025)
Quantum 9, 1769 (2025)
arXiv:2504.19319
arXiv:2508.14979
arXiv:2510.07305
arXiv:2510.05531
Nature Communications volume 17, Article number: 373(2026)
arXiv:2603.18136
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