Quantum Fisher information from randomized measurements

TL;DR

This paper introduces a method to estimate lower bounds of quantum Fisher information using randomized measurements, enabling practical assessment of entanglement and quantum properties in many-body systems.

Contribution

The authors develop a protocol to accurately estimate QFI lower bounds via randomized measurements, with convergence guarantees and measurement efficiency analysis.

Findings

Protocol accurately estimates QFI lower bounds

Method applies to coupled qubits and collective spins

Provides measurement efficiency and accuracy analysis

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.