Related papers: Limit theorems for Quantum Trajectories
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…
Quantum trajectories are Markov processes describing the evolution of a quantum system subject to indirect measurements. They can be viewed as place dependent iterated function systems or the result of products of dependent and non…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of…
In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…
We consider N single server infinite buffer queues with service rate \beta. Customers arrive at rate N\alpha, choose L queues uniformly, and join the shortest. We study the processes R^N for large N, where R^N_t(k) is the fraction of queues…
Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called "Stochastic Schr\"odinger Equations",…
We obtain some rigorous results on limit theorems for quantum walks driven by many coins introduced by Brun et al. in the long time limit. The results imply that whether the behavior of a particle is quantum or classical depends on the…
Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law…
Motivated by a recent work of Benoist and Quint and extending results from the PhD thesis of the third author, we obtain limit theorems for products of independent and identically distributed elements of GLd (R), such as the…
In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit…
We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties and concentration inequalities for the environment as seen…
The evolution of a quantum system undergoing repeated indirect measurements naturally leads to a Markov chain on the set of states which is called a quantum trajectory. In this paper we consider a specific model of such a quantum trajectory…
Beyond their use as numerical tools, quantum trajectories can be ascribed a degree of reality in terms of quantum measurement theory. In fact, they arise naturally from considering continuous observation of a damped quantum system. A…
We prove distributional limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from non-integrable observables over certain piecewise…
Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…
"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…