Multi-parameter quantum metrology with discrete-time quantum walks

TL;DR

This paper explores multi-parameter quantum estimation using discrete-time quantum walks, deriving Fisher information expressions, analyzing parameter accessibility, and applying results to models like the discretized Dirac equation.

Contribution

It provides an analytic expression for the quantum Fisher information matrix in quantum walks and investigates the classicality of the two-parameter coin model.

Findings

Only two of three coin parameters are accessible.

The two-parameter coin model is asymptotically classical.

Application to estimating charge and mass in the Dirac model.

Abstract

We address multi-parameter quantum estimation for one-dimensional discrete-time quantum walks and its applications to quantum metrology. We use the quantum walker as a probe for unknown parameters encoded on its coin degrees of freedom. We find an analytic expression of the quantum Fisher information matrix for the most general coin operator, and show that only two out of the three coin parameters can be accessed. We also prove that the resulting two-parameter coin model is asymptotically classical i.e. the Uhlmann curvature vanishes. Finally, we apply our findings to relevant case studies, including the simultaneous estimation of charge and mass in the discretized Dirac model.