Complementarity and quantum walks
Viv M. Kendon, Barry Cyril Sanders · Physical Review A · 2005
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.