Complementarity and quantum walks

Kendon, Viv and Sanders, Barry C. (2005) Complementarity and quantum walks. Physical Review A, 71 (2). 022307. ISSN 1050-2947 (https://doi.org/10.1103/PhysRevA.71.022307)

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Abstract

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.

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