Related papers: A method for exponential operator decomposition
This thesis examines the empirical mode decomposition (EMD), a method for decomposing multicomponent signals, from a modern, both theoretical and practical, perspective. The motivation is to further formalize the concept and develop new…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a…
Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…
We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
A scheme is presented to decompose the exponential of a two-body operator in a discrete sum over exponentials of one-body operators. This discrete decomposition can be used instead of the Hubbard-Stratonovich transformation in…
We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…
We investigate properties of exponential operators preserving the particle number using combinatorial methods developed in order to solve the boson normal ordering problem. In particular, we apply generalized Dobinski relations and methods…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
The Kalman decomposition for Linear Quantum Stochastic Systems in the real quadrature operator representation, that was derived indirectly in [1] by the authors, is derived here directly, using the "one-sided symplectic" SVD-like…
In this tutorial, exponentiation and factorization (decomposition) formulas are derived and discussed for common matrix operators that arise in studies of classical dynamics, linear and nonlinear optics, and special relativity. To…
Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…
By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…
By means of a fixed point method we discuss the deformation of operator means and multivariate means of positive definite matrices/operators. It is shown that the deformation of an operator mean becomes again an operator mean. The means…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…