Phase estimation in driven discrete-time quantum walks

Quantum walks have been shown to be important for quantum metrological tasks, in particular for the estimation of the evolution parameters of the walk. In this work, we address the enhancement of this parameter estimation using the driven discrete-time quantum walk (DDTQW), which is a variant of the discrete-time quantum walk with multiple walkers. DDTQW has two regimes based on the interference between the walker number, i.e., phase matched and phase mismatched. We derive an expression for the quantum Fisher information (QFI) in the phase-matched regime of DDTQW driven using the squeezing operator, demonstrating an exponential increase in QFI. In the phase-mismatched regime, QFI varies as t2, consistent with previous studies. Our analysis shows that parameter estimation can be improved by driving the walk using squeezing operators.