Quantum Fisher information from randomized measurements
Abstract
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement in quantum many-body-systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
Cite
@article{arxiv.2105.13164,
title = {Quantum Fisher information from randomized measurements},
author = {Aniket Rath and Cyril Branciard and Anna Minguzzi and Benoît Vermersch},
journal= {arXiv preprint arXiv:2105.13164},
year = {2023}
}
Comments
7 + 10 pages with 3 + 3 figures. Accepted version with additional analytical expressions for statistical errors of arbitrary order polynomials of the density matrix estimated via classical shadows. Code available at https://github.com/bvermersch/RandomMeas