Related papers: The meeting problem in the quantum random walk
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…
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…
We show analytically that particle trapping appears in a quantum process called "quantum walk", in which the particle moves macroscopically correlating to the inner states. It has been well known that a particle in the ``Hadamard walk" with…
We define a random walk of a particle in $\mathbb{R}^3$ where the space is rotating. The particle is not glued to the space and will collide with it at random times, resulting in changes in its velocity and direction. After many collisions,…
We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are…
Quantum walk acts obviously different from its classical counterpart, but decoherence will lessen and close the gap between them. To understand this process, it is necessary to investigate the evolution of quantum walk under different…
Asymptotic dynamics of a Hadamard walk of two non-interacting quantum particles on a dynamically percolated finite line or a circle is investigated. We construct a basis of the attractor space of the corresponding random-unitary dynamics…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero stationary distributions (localization), thus distinguishing themselves…
Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical…
This paper explores the entanglement dynamics generated by interacting two-particle quantum walks on degree-regular and -irregular graphs. We performed spectral analysis of the time-evolution of both the particle probability distribution…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
We investigate continuous-time quantum walks of two indistinguishable particles [bosons, fermions or hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are well consistent with…
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In…
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…
We study the motion of M particles performing a quantum walk on the line. Under various conditions on the initial coin states for quantum walkers controlled by the Hadamard operator, we give theoretical criterion to observe the quantum…