Related papers: Quantum information spreading in a disordered quan…
The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…
Propagation and interference of quantum-mechanical particles comprise an important part of elementary processes in quantum physics, and their essence can be modeled using a quantum walk, a mathematical concept that describes the motion of a…
The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
We present a framework for quantifying information flow within general quantum processes. For this purpose, we introduce the signaling power of quantum channels and discuss its relevant operational properties. This function supports…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior…
We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The…
We study the effects of interparticle interactions and power-law tunneling couplings on quantum walks executed by both a single one and a pair of hard-core bosons moving in clean and disordered one-dimensional lattices. For this purpose, we…
We address routing of classical and quantum information over quantum network, and show how to exploit chirality to achieve nearly optimal and robust transport. In particular, we prove how continuous time chiral quantum walks over a minimal…
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
A quantum walk in an ordered medium exhibits ballistic propagation. A related process is the driven quantum walk, in which the number of walkers varies along the propagation. In this work, we show that a driven quantum walk of biphoton…
We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…
We develop techniques to probe the dynamics of quantum information, and implement them experimentally on an IBM superconducting quantum processor. Our protocols adapt shadow tomography for the study of time evolution channels rather than of…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…