Hilbert space-valued Gaussian processes, and quantum states

2024/05/05 by Palle E. T. Jørgensen, Jorgensen, Palle E. T., James Tian +1 · 1 citation
Physics and Astronomy · Computer Science · #Statistical Mechanics and Entropy #Gaussian Processes and Bayesian Inference #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.2405.02796

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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• Random Operator-Valued Kernels and Moment Dilations

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