We investigate how the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, can be exploited as a powerful and easily computable tool for quantum phase estimation in a n-qubit system. We find that, when both the HSS and quantum Fisher information (QFI) are computed with respect to the phase parameter encoded into the initial state of the n-qubit register, the zeros of the HSS dynamics are essentially the same as those of the QFI dynamics. Moreover, the positivity (negativity) of the time-derivative of the HSS exactly coincides with the positivity (negativity) of the time-derivative of the QFI. Our results also provide strong evidence for contractivity of the HSS under completely positive and trace preserving maps in high-dimensional systems, as predicted in previous studies.
Cite
@article{arxiv.2009.06050,
title = {Hilbert-Schmidt speed as an efficient tool in quantum metrology},
author = {Hossein Rangani Jahromi and Rosario Lo Franco},
journal= {arXiv preprint arXiv:2009.06050},
year = {2020}
}