## File(s) under permanent embargo

# Parameter estimation with reluctant quantum walks

The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the line, or on a finite ring. Two different coin reshuffling actions are presented, with the real parameter

*θ*to be estimated being identified either with the angular argument of an orthogonal reshuffling matrix, or the phase of a unitary reshuffling matrix, acting in a 2 state coin space, respectively. We provide analytic results for the probability distribution for a quantum walker to be displaced by d units from its initial position after*k*steps. For*k*large, we show that the likelihood is sharply peaked at a displacement determined by the ratio*d*/*k*, which is correlated with the reshuffling parameter*θ*. We suggest that this ‘reluctant walker’ behaviour provides the framework for maximum likelihood estimation analysis, allowing for robust parameter estimation of*θ*via measurement of the walker ‘reluctance index’*r*=*d*/*k*.## History

## ISSN

2331-8422## Department/School

School of Natural Sciences## Publisher

Cornell University## Place of publication

online## Preprint server

arXiv## Repository Status

- Restricted