Sub-Quantum Fisher Information

TL;DR

This paper introduces the sub-Quantum Fisher Information (sub-QFI), a computationally efficient lower bound on the QFI that retains key properties, making it useful for quantum sensing and metrology.

Contribution

The work defines and analyzes the sub-QFI, demonstrating its faithfulness to the QFI and its applicability as an efficient surrogate in quantum information tasks.

Findings

Sub-QFI can be estimated efficiently on quantum computers.

Sub-QFI shares the same global extrema as the QFI.

Sub-QFI serves as a measure of coherence, asymmetry, and purity loss.

Abstract

The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we analyze a lower bound on the QFI which we call the sub-Quantum Fisher Information (sub-QFI). The bound can be efficiently estimated on a quantum computer for an $n$-qubit state using $2n$ qubits. The sub-QFI is based on the super-fidelity, an upper bound on Uhlmann's fidelity. We analyze the sub-QFI in the context of unitary families, where we derive several crucial properties including its geometrical interpretation. In particular, we prove that the QFI and the sub-QFI are maximized for the same optimal state, which implies that the sub-QFI is faithful to the QFI in the sense that both quantities share the same global extrema. Based on this faithfulness, the sub-QFI acts as an efficiently computable surrogate for the QFI for quantum sensing and quantum metrology applications. Finally, we provide additional meaning to the sub-QFI as a measure of coherence, asymmetry, and purity loss.