Hilbert space-valued Gaussian processes, and quantum states
Quantum Physics
2025-03-04 v2 Functional Analysis
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.
Cite
@article{arxiv.2405.02796,
title = {Hilbert space-valued Gaussian processes, and quantum states},
author = {Palle E. T. Jorgensen and James Tian},
journal= {arXiv preprint arXiv:2405.02796},
year = {2025}
}