Hilbert space-valued Gaussian processes, and quantum states

TL;DR

This paper introduces new theoretical insights and methods for analyzing Hilbert space-valued Gaussian processes and quantum states, with applications in quantum information and measurement theory.

Contribution

It provides explicit covariance analysis, optimization techniques for quantum gates, and novel results for quantum measurements and inverse problems.

Findings

Explicit covariance analysis for Hilbert space-valued Gaussian processes

Optimization results for quantum gates

New insights into positive operator-valued measures (POVMs)

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.