Related papers: Hilbert space-valued Gaussian processes, and quant…
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and…
In recent work (Nii et al., arXiv:1603.06291; Iinuma et al., Phys. Rev. A 93, 032104 (2016)(arXiv:1510.03958)) we have studied the relation between experimental outcomes and the physical properties represented by Hilbert space operators of…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
A new non-parametric method based on Gaussian Processes was proposed recently to measure the Hubble constant $H_0$. The freedom in this approach comes in the chosen covariance function, which determines how smooth the process is and how…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…
Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…
In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…
Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
A new notion of stochastic germs for quantum processes is introduced and a characterisation of the stochastic differentials for positive definite (PD) processes is found in terms of their germs for arbitrary Ito algebra. A representation…
In this thesis we study symmetric structures in Hilbert spaces known as symmetric informationally complete positive operator-valued measures (SIC-POVMs), mutually unbiased bases (MUBs), and MUB-balanced states. Our tools include symmetries…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
We consider the convex sets of QO's (quantum operations) and POVM's (positive operator valued measures) which are covariant under a general finite-dimensional unitary representation of a group. We derive necessary and sufficient conditions…