# Decoherence in a one-dimensional quantum walk

@article{Annabestani2010DecoherenceIA, title={Decoherence in a one-dimensional quantum walk}, author={Mostafa Annabestani and Seyed Javad Akhtarshenas and Mohamad Reza Abolhassani}, journal={Physical Review A}, year={2010}, volume={81}, pages={032321} }

In this article we study decoherence in the discrete-time quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al. [Phys. Rev. A 67, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is…

## 32 Citations

Brun-Type Formalism for Decoherence in Two Dimensional Quantum Walks

- Physics, Mathematics
- 2011

We study decoherence in the quantum walk on the xy-plane. We generalize the method of decoherent coin quantum walk, introduced by [T.A. Brun, et.al, Phys.Rev.A 67 (2003) 032304],which could be…

Incoherent tunneling effects in a one-dimensional quantum walk

- Physics
- 2016

In this article we investigate the effects of shifting position decoherence, arising from the incoherent tunneling effect in the experimental realization of the quantum walk, on the one-dimensional…

Transfiguration of Quantum Walks on a line

- Physics
- 2018

We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time…

Limit theorems for decoherent two dimensional quantum walks

- Physics, MathematicsQuantum Inf. Process.
- 2012

The model with decoherence operators introduced by Brun et al. (Phys Rev A 67:032304, 2003) is considered which has recently been considered in the two-dimensional setting by Ampadu to obtain the limit of the decoherent quantum walk.

On the von Neumann entropy of certain quantum walks subject to decoherence†

- Mathematics, PhysicsMathematical Structures in Computer Science
- 2010

It is proved that the von Neumann entropy of the total density operator converges to its maximum value, which means that any level of decoherence greater than zero forces the system to become completely ‘disentangled’ eventually.

Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

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- 2014

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect…

One-dimensional quantum walks subject to next-nearest-neighbour hopping decoherence

- Physics, Computer ScienceQuantum Inf. Process.
- 2015

The diffusive behaviours of quantum walks are sub-ballistic and the distributions of position exhibit three peaks when the decoherence effects only come from the bilateral hopping operation, quite different from those of the previous non-unitary quantum walks.

The Elephant Quantum Walk

- Computer Science, PhysicsPhysical Review A
- 2018

We explore the impact of long-range memory on the properties of a family of quantum walks in a one-dimensional lattice and discrete time, which can be understood as the quantum version of the…

Entropy analysis of the discrete-time quantum walk under bit-flip noise channel

- Physics
- 2021

Abstract We study the behavior of tunable one-dimensional discrete-time quantum walk (DTQW) in the presence of decoherence modelled by the flip-bit noise channel. By varying the noise intensity, we…

Asymptotic evolution of quantum walks on the N-cycle subject to decoherence on both the coin and position degrees of freedom

- Physics
- 2011

Consider a discrete-time quantum walk on the N-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we…

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