Decoherence in the quantum walk on the line

Details Decoherence in the quantum walk on the line Decoherence in the quantum walk on the line

2004-03-26

arxiv.org/abs/quant-ph/0403192v2

Phys. A, vol 347C, pp. 137-152 (2005)

Physics

Quantum Physics

Elsevier style, 18 pages. New enhanced version with more material: new title, a new section was added and the discussion was u

Scientific paper

10.1016/j.physa.2004.08.070

We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical diffusive behavior. In the case of measurements, we show that the diffusion coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. When links between neighboring sites are randomly broken with probability $p$ per unit time, the evolution becomes decoherent after a characteristic time that scales as $1/p$. The fact that the quadratic increase of the variance is eventually lost even for very small frequencies of disrupting events, suggests that the implementation of a quantum walk on a real physical system may be severely limited by thermal noise and lattice imperfections.

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