Related papers: P\'olya number of continuous-time quantum walks
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
We show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding them away from equilibrium is exponentially suppressed, with a…
Measurements on a quantum particle unavoidably affect its state, since the otherwise unitary evolution of the system is interrupted by a non-unitary projection operation. In order to probe measurement-induced effects in the state dynamics…
We prove analytical results showing that decoherence can be useful for mixing time in a continuous-time quantum walk on finite cycles. This complements the numerical observations by Kendon and Tregenna (Physical Review A 67 (2003), 042315)…
A study of persistence dynamics is made for the first time in a quantum system by considering the dynamics of a quantum random walk. For a discrete walk on a line starting at $x=0$ at time $t=0$, the persistence probability $P(x,t)$ that a…
We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…
We study quantum walks of many non-interacting particles on a beam splitter array, as a paradigmatic testing ground for the competition of single- and many-particle interference in a multi-mode system. We derive a general expression for…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
In this work, we study open quantum random walks, as described by S. Attal et al. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the…
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…
The outcome of continuously measuring a quantum system is a string of data whose intricate correlation properties reflect the underlying quantum dynamics. In this paper we study the role of these correlation in reconstructing the…
This paper is devoted to the study of continuous-time processes known as continuous-time open quantum walks (CTOQWs). A CTOQW represents the evolution of a quantum particle constrained to move on a discrete graph, but also has internal…
The very large transverse momenta and large multiplicities available in present LHC experiments on pp collisions allow a much closer look at the corresponding distributions. Some time ago we discussed a possible physical meaning of apparent…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
Recurrence time quantifies the duration required for a physical system to return to its initial state, playing a pivotal role in understanding the predictability of complex systems. In quantum systems with subspace measurements, recurrence…
Following Hales (2018), the evolution of P\'olya's urn may be interpreted as a walk, a P\'olya walk, on the integer lattice $\mathbb{N}^2$. We study the visibility properties of P\'olya's walk or, equivalently, the divisibility properties…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical…