Related papers: Decomposition of Quantum Markov Chains and Its App…
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
Information-theoretic arguments focus on modeling the reliability of information transmission, assuming availability of infinite data at sources, thus ignoring randomness in message generation times at the respective sources. However, in…
We study fixed-policy evaluation for finite Markov chains that may be reducible and periodic. Classical evaluation methods with gain and bias decomposition are not always diagnostic: the gain records only invariant Ces\`aro averages, while…
Markov-modulated Brownian motion is a popular tool to model continuous-time phenomena in a stochastic context. The main quantity of interest is the invariant density, which satisfies a differential equation associated with the quadratic…
We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a…
We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g.…
We propose a new Kalikow decomposition for continuous time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation…
This paper presents a systematic method to decompose uncertain linear quantum input-output networks into uncertain and nominal subnetworks, when uncertainties are defined in SLH representation. To this aim, two decomposition theorems are…
We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved,…
In a diffusion-based molecular communication network, transmitters and receivers communicate by using signalling molecules (or ligands) in a fluid medium. This paper assumes that the transmitter uses different chemical reactions to generate…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
Quantum memory systems are vital in quantum information processing for dependable storage and retrieval of quantum states. Inspired by classical reliability theories that synthesize reliable computing systems from unreliable components, we…
Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…
Bottom-up coarse-grained (CG) modeling expands the spatial and temporal scales of molecular simulation by seeking a reduced, thermodynamically consistent representation of an atomistic model. Developments in CG theory have largely focused…
We develop dynamical non-Markovian description of quantum computing in weak coupling limit, in lowest order approximation. We show that long range memory of quantum reservoir produces strong interrelation between structure of noise and…
Building large-scale quantum communication networks has its unique challenges. Here, we demonstrate that a network-wide synergistic usage of quantum memories distributed in a quantum communication network offers a fundamental advantage. We…