Related papers: Diagonal Couplings of Quantum Markov Chains
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
By implementing a quantum repeater protocol, our aim in this paper is the production of entanglement between two two-level atoms locating far from each other. To make our model close to experimental realizations, the atomic and field…
In complex dynamical systems, the detection of coupling and its direction from observed time series is a challenging task. We study coupling in coupled Duffing oscillator systems in regular and chaotic dynamical regimes. By observing the…
Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using…
With non-invasive methods, we investigate ground and excited states of a lateral quantum dot. Charge detection via a quantum point contact is used to map the dot dynamics in a regime where the current through the dot is too low for…
Synchronization is an important dynamical phenomenon in coupled nonlinear systems, which has been studied extensively in recent years. However, analysis focused on individual orbits seems hard to extend to complex systems while a global…
In the present paper we study a unified approach for Quantum Markov Chains. A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic…
We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the…
We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define…
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently…
The asymptotic dynamics of quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space on which the resulting quantum Markov chain is…
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included…
Traditionally, quantum state correlation can be obtained with calculations on a state density matrix already known. Here, we propose a model with which correlations of unknown quantum states can be obtained. There are no needs of classical…
We investigated the entanglement in a diluted magnetic semiconductor quantum dot, crucial for quantum technologies. Despite their potential, these systems exhibit low extraction rates. We explore self-assembled InGaAs quantum dots, focusing…
We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the…
We propose a methodology to parallelize Hamiltonian Monte Carlo estimators. Our approach constructs a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These…
We study quantum entanglement for CAR systems. Since the subsystems of disjoint regions are not independent for CAR systems, there are some distinct features of quantum entanglement which cannot be observed in tensor product systems. We…
The quantum dot spin chain system is vital for quantum simulation and studying collective electron behaviors, necessitating an understanding of its mechanisms and control protocols. Chapter 1 introduces key concepts, focusing on the…
A notion of entangled Markov chain was introduced by Accardi and Fidaleo in the context of quantum random walk. They proved that, in the finite dimensional case, the corresponding states have vanishing entropy density, but they did not…