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Within a special multi-coin quantum walk scheme we analyze the effect of the entanglement of the initial coin state. For states with a special entanglement structure it is shown that this entanglement can be meausured with the mean value of…

We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the…

The concept of a random walk on a finite group converging to random - and a way of measuring the distance to random after $k$ transitions - is generalised from the classical case to the case of random walks on finite quantum groups. A…

We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…

The lonely runner conjecture of Wills and Cusick asserts that if $n$ runners with distinct constant speeds run around a a circular unit length track, starting at a common time and place, then each runner will at some time be separated by a…

This study investigates unitary equivalent classes of one-dimensional quantum walks. We prove that one-dimensional quantum walks are unitary equivalent to quantum walks of Ambainis type and that translation-invariant one-dimensional quantum…

Quantum walks are the quantum mechanical analogue of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and…

We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying…

We investigate the splitting probability of a monitored continuous-time quantum walk with two targets and show that, in stark contrast to a classical random walk, it exhibits a nonanalytic, phase-transition-like behavior controlled by the…

We study a quantum walk (QW) whose time evolution is induced by a random walk (RW) first introduced by Szegedy (2004). We focus on a relation between recurrent properties of the RW and localization of the corresponding QW. We find the…

We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure $\mu_n$ on the space of $n$-paths, and the $\mu_n$ in turn induce a quantum measure $\mu$ on the cylinder sets…

We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…

The lackadaisical quantum walk, a quantum analog of the lazy random walk, is obtained by adding a weighted self-loop transition to each state. Impacts of the self-loop weight $l$ on the final success probability in finding a solution make…

Quantum walks have wide applications in quantum information, such as universal quantum computation, so it is important to explore properties of quantum walks thoroughly. We propose a novel method to implement discrete-time quantum walks…

Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…

In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with…

We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…

We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…