Related papers: Covariant Quantum Dynamical Semigroups: Unbounded …

We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary incoherent driving. The construction is based on…

A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type…

We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…

Supervised learning algorithms take as input a set of labelled examples and return as output a predictive model. Such models are used to estimate labels for future, previously unseen examples drawn from the same generating distribution. In…

We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle,…

Efficient methods for the description of the non-Markovian dynamics of open systems play an important role in many proposed applications of quantum mechanics. Here we review some of the most important tools that are based on the projection…

Necessary and sufficient conditions are given for a substochastic semigroup on $L^1$ obtained through the Kato--Voigt perturbation theorem to be either stochastic or strongly stable. We show how such semigroups are related to piecewise…

The study of Markov models is central to control theory and machine learning. A quantum analogue of partially observable Markov decision process was studied in (Barry, Barry, and Aaronson, Phys. Rev. A, 90, 2014). It was proved that…

We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior of maps that combine amplitude damping, inverse amplitude damping, and pure dephasing. We show that mixing non-unital…

A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via…

The Reshetikhin - Turaeve approach to topological invariants of three - manifolds is generalized to quantum supergroups. A general method for constructing three - manifold invariants is developed, which requires only the study of the…

A quantum Markov semigroup can be represented via classical diffusion processes solving a stochastic Schr\"odinger equation. In this paper we first prove that a quantum Markov semigroup is irreducible if and only if classical diffusion…

We give upper and lower estimates of densities of convolution semigroups of probability measures under explicit assumptions on the corresponding Levy measure and the Levy--Khinchin exponent. We obtain also estimates of derivatives of…

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions…

We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard GKLS generator. These…

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…

Investigations of quantum and mesoscopic thermodynamics force one to answer two fundamental questions associated with the foundations of statistical mechanics: (i) how does macroscopic irreversibility emerge from microscopic reversibility?…

A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…

Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations…

In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…