Related papers: Markovian Marignals
An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
The paper identifies families of quasi-stationary initial conditions for infinite Brownian particle systems within a large class and provides a construction of the particle systems themselves started from such initial conditions. Examples…
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…
Entangled states are in conflict with a general physical principle which expresses that a composite entity exists if and only if its components also exist, and the hypothesis that pure states represent the actuality of a physical entity,…
We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics…
An entangled quantum state of two or more particles or objects exhibits some of the most peculiar features of quantum mechanics. Entangled systems cannot be described independently of each other even though they may have an arbitrarily…
We address the problem of quantifying the non-Markovian character of quantum time-evolutions of general systems in contact with an environment. We introduce two different measures of non-Markovianity that exploit the specific traits of…
Modern quantum information theory provides new tools for investigating the decoherence-induced "classicality" of open quantum systems. Recent observation that almost all quantum states bear non-classical correlations [A. Ferraro {\it et…
The study of the entanglement entropy and entanglement spectrum has proven to be very fruitful in identifying topological phases of matter. Typically, one performs numerical studies of finite-size systems. However, there are few rigorous…
In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This…
Markovianity lies at the heart of communication problems. This in turn makes the information-theoretic characterization of Markov processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary…
In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite…
A consequence of Ornstein theory is that the infinite entropy flows associated with Poisson processes and continuous-time irreducible Markov chains on a finite number of states are isomorphic as measure-preserving systems. We give an…
Quantum mechanics allows systems to be entangled with each other, which results in stronger than classical correlations. Many methods of identifying entanglement have been proposed over years, most of which are based on violating some…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
We show that the presence of finite-size monopoles can lead to a number of interesting physical processes involving quantum entanglement of charges. Taking as a model the classical solution of the N=2 SU(2) Yang-Mills theory, we study…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…