Decoherence in the quantum walk on the line: I - Measurements
A. Romanelli, R. Siri, Gonzalo Abal, A. Auyuanet, R. Donangelo · arXiv (Cornell University) · 2004
We investigate the quantum walk on the line when decoherence is introduced through simultaneous measurements of the chirality and the particle position. This decoherence drives the system to a classical diffusive behavior, for which we have obtained analytical expressions for its diffusion coefficient. We show that this coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. Through an association of the measurement processes to the collisions in Brownian motion, we show that this treatment provides a smooth connection between the pure classical and quantum limits.