Decoherence in a one-dimensional quantum walk

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 subjected to decoherence.

Figure 1

Possible situations for site n when there are (a) no broken links, (b) the link to the left of the site is broken, (c) the link to the right of the site is broken, and (d) both links are broken. The arrows indicate the direction of the probability flux associated to the L,R components.

Figure 2

The $K(p)$ versus $p$.