Related papers: Asymptotic properties of quantum Markov chains
What can one infer about the dynamical evolution of quantum systems just by symmetry considerations? For Markovian dynamics in finite dimensions, we present a simple construction that assigns to each symmetry of the generator a family of…
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing…
It was recently pointed out that identifiability of quantum random walks and hidden Markov processes underlie the same principles. This analogy immediately raises questions on the existence of hidden states also in quantum random walks and…
Coupling any interacting quantum mechanical system to gravity in one dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantized, even though the gravity sector is free of any quantum…
In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects. The completely positive reduced dynamical map can…
We study the asymptotic behavior of continuous-time, time-inhomogeneous Markovian quantum dynamics in a stationary random environment. Under mild faithfulness and eventually positivity-improving assumptions, the normalized evolution…
We investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a…
Completely positive maps are useful in modeling the discrete evolution of quantum systems. Spectral properties of operators associated with such maps are relevant for determining the asymptotic dynamics of quantum systems subjected to…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…
We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in…
Coupling any interacting quantum mechanical system to gravity in one (time) dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantised, even though the gravity sector is free of any quantum…
In this paper, we consider continuous-time Markov chains with a finite state space under nonlinear expectations. We define so-called Q-operators as an extension of Q-matrices or rate matrices to a nonlinear setup, where the nonlinearity is…
If $(C_n)$ is a Markov chain on a discrete state space ${\mathcal{S}}$, a Markov chain $(C_n,M_n)$ on the product space ${\mathcal{S}}\times{\mathcal{S}}$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov…
Accessing the physical mechanisms behind non-Markovian phenomena in open quantum dynamics requires the study of the statistical properties of the joint system-environment dynamics. This is impossible at the level of the reduced dynamics of…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…
A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over a infinite state space can be identified by a…