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Quantum Physics
Title: Canonical data-reconstructions via kernels, Hilbert space-valued Gaussian processes, and quantum states
(Submitted on 5 May 2024)
Abstract: We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit covariance analysis for Hilbert space-valued Gaussian processes, (ii) optimization results for quantum gates (from quantum information), (iii) new results for positive operator-valued measures (POVMs), and (iv) a new approach/result in inverse problems for quantum measurements.
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