Related papers: An introduction to decoupling and harmonic analysi…
We revisit the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. {\bf 94},…
In the studies of the squeezing it is customary to focus more attention on the particular squeezed states and their evolution than on the dynamical operations that could squeeze simultaneously some wider families of quantum states,…
The task of decoupling, i.e., removing unwanted interactions in a system Hamiltonian and/or couplings with an environment (decoherence), plays an important role in controlling quantum systems. There are many efficient decoupling schemes…
We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We illustrate our approach with a concrete…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
Quantum information processing with multi-level systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
We review some important algebraic structures which appear in a priori remote areas of Mathematics, such as control theory, numerical methods for solving differential equations, and renormalization in Quantum Field Theory. Starting with…
Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However, our understanding of the…
We unite two themes in dyadic analysis and number theory by studying an analogue of the failure of the Hasse principle in harmonic analysis. Explicitly, we construct an explicit family of measures on the real line that are $p$-adic and…
Hubbard model is an important model in theory of strongly correlated electron systems. In this contribution we introduce this model along with numerically exact method of diagonalization of the model.
In this paper, we remind previous results about the tilings $\{p,q\}$ of the hyperbolic plane. We introduce two new ways to split the hyperbolic plane in order to algorithmically construct the tilings $\{p,q\}$ when $q$ is odd.
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
We develop a toolbox for proving decouplings into boxes with diameter smaller than the canonical scale. As an application of this new technique, we solve three problems for which earlier methods have failed. We start by verifying the small…
Disentangling the explanatory factors in complex data is a promising approach for generalizable and data-efficient representation learning. While a variety of quantitative metrics for learning and evaluating disentangled representations…
This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same…
We prove a restricted projection theorem for Borel subsets of $\mathbb{Q}_p^n$ in the regime $p>n$. This generalizes results of Gan-Guo-Wang in the real setting. Our result is effective in the sense that explicit constants are obtained for…