Related papers: Decoherence in Quantum Walks on the Hypercube
Quantum coherence is a fundamental characteristic to distinguish quantum systems from their classical counterparts. Though quantum coherence persists in isolated non-interacting systems, interactions inevitably lead to decoherence, which is…
The decoherence mechanism signals the limits beyond which the system dynamics approaches the classical behavior. We show that in some cases decoherence may also signal the limits beyond which the system dynamics has to be described by…
Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible.…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
Despite being created through a fundamentally quantum-mechanical process, cosmological structures have not yet revealed any sign of genuine quantum correlations. Among the obstructions to the direct detection of quantum signatures in…
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…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
In this paper, we present a quantum Bernoulli noises approach to quantum walks on hypercubes. We first obtain an alternative description of a general hypercube and then, based on the alternative description, we find that the operators…
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 study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
A quantum central limit theorem for a continuous-time quantum walk on a homogeneous tree is derived from quantum probability theory. As a consequence, a new type of limit theorems for another continuous-time walk introduced by the walk is…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
The performance of modern quantum devices in communication, metrology or microscopy relies on the quantum-classical interaction which is generally described by the theory of decoherence. Despite the high relevance for long coherence times…
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…