Generalized Measure of Quantum Fisher Information

TL;DR

This paper introduces a new, efficiently computable lower bound on quantum Fisher information (QFI) suitable for near-term quantum devices, generalizing the standard QFI for subnormalized states and aiding in quantum parameter estimation.

Contribution

It proposes a novel lower bound on QFI that is computationally efficient and applicable to subnormalized states, extending the standard QFI measure.

Findings

The bound is efficiently computable on near-term quantum devices.

It satisfies the canonical criteria of a QFI measure.

Demonstrates utility for estimating QFI in unitary families of states.

Abstract

In this work, we present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices. This bound itself is of interest, as we show that it satisfies the canonical criteria of a QFI measure. Specifically, it is essentially a QFI measure for subnormalized states, and hence it generalizes the standard QFI in this sense. Our bound employs the generalized fidelity applied to a truncated state, which is constructed via the $m$ largest eigenvalues and their corresponding eigenvectors of the probe quantum state $\rho_{\theta}$. Focusing on unitary families of exact states, we analyze the properties of our proposed lower bound, and demonstrate its utility for efficiently estimating the QFI.