Related papers: Universal dynamical scaling laws in three-state qu…
The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two…
We investigated discrete time quantum walks with an arbitrary initial state $\mid\Psi_{0}(\theta,\phi,\varphi)\rangle=\cos\theta e^{i\phi}\mid0L\rangle+\sin\theta e^{i\varphi}\mid0R\rangle$ with a U(2) coin $U(\alpha,\beta,\gamma)$. We…
We have studied how decoherence affects a quantum walk on the line. As expected, it is highly sensitive, consisting as it does of an extremely delocalized particle. We obtain an expression for the rate at which the standard deviation falls…
We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As…
We study the evolution of quantum correlations in two-particle discrete-time non-unitary quantum walks on a line with gain and loss. The two particles are initially prepared in a maximally entangled state and evolve independently. Using…
We derive analytical results for continuous-time quantum walks from a new class of initial states with tunable delocalization. The dynamics are governed by a Hamiltonian with complex hopping amplitudes. We provide closed-form equations for…
Distributed systems in which concurrent proposals are mutually exclusive face a fundamental stability constraint under network delay. In open systems where global state progression is event-driven rather than round-driven, propagation delay…
We investigate time-dependent properties of a single particle model in which a random walker moves on a triangle and is subjected to non-local boundary conditions. This model exhibits spontaneous breaking of a Z_2 symmetry. The reduced size…
Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete…
We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…
Fix a strictly positive measure $W$ on the $d$-dimensional torus $\bb T^d$. For an integer $N\ge 1$, denote by $W^N_x$, $x=(x_1, ..., x_d)$, $0\le x_i <N$, the $W$-measure of the cube $[x/N, (x+\mb 1)/N)$, where $\mb 1$ is the vector with…
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…
We investigate how quantum coherence scales and is redistributed in quantum communication protocols, using superdense coding and quantum teleportation as paradigmatic case studies. Employing the relative entropy of coherence as a…
The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…
We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of…
Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multi-species annihilating random walk transition found at zero branching rate previously is investigated now concerning…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson…
Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…