Improving quantum walk metrology with split-step quantum walk

Abstract: A new estimation scheme based on the split-step quantum walk (SSQW) revealed that by just setting a single parameter, SSQW can potentially achieve quantum Crame\'r-Rao bound in multiparameter estimation. This parameter even does not involve the parameterization but the initial state and unlike ordinary Quantum walk (OQW) there is no necessity for an entangled initial states or even a parameter dependent initial state. The rigorous analytic equations derived in this study revealed that SSQW surpasses OQW in achievable precision of multiparameter estimation in almost all possible scenarios. Furthermore, in single parameter estimation, the extra parameter can be used to tune the dynamics of the walk in such a way to enhance the precision of the estimation through maximizing the elements of quantum Fisher information matrix. The results of this study indicate that SSQW can remarkably improve the estimation schemes through its rich topological properties.