Complementarity and quantum walks (7 pages)

Frederick W. Strauch

Amanda C. Oliveira

Dmitry Solenov, Leonid Evgenevich Fedichkin

Renato Portugal

Viv M. Kendon

By generalizing a quantum walk to include measurement of the path taken by the quantum walker, we show that quantum walks interpolate between a fully coherent quantum dynamics and a classical random walk, depending on how strongly the walker’s coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity.

Viv M. Kendon, Barry C. Sanders

We show that quantum walks interpolate between a coherent ``wave walk'' and a random walk depending on how strongly the walker's coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity, which is manifested as a tradeoff between knowledge of which path the walker takes vs the sharpness of the interference pattern. A physical implementation of a quantum walk (the quantum quincunx) should thus have an identifiable walker and the capacity to demonstrate the interpolation between wave walk and random walk depending on the strength of measurement.