Opportunities and Limitations in Broadband Sensing

TL;DR

This paper introduces the concept of integrated quantum Fisher information to analyze the fundamental tradeoffs in broadband sensing, revealing how sensitivity in one frequency range affects others and identifying optimal protocols for rapid wideband detection.

Contribution

It develops a theoretical framework using integrated quantum Fisher information to understand limitations and potentials in broadband quantum sensing protocols.

Findings

Sensitivity tradeoffs across frequency ranges are quantified by new inequalities.

Protocols with large phase accumulation can achieve quadratic growth in integrated QFI.

Optimal protocols enable rapid detection of signals over wide bandwidths.

Abstract

We consider estimating the magnitude of a monochromatic AC signal that couples to a two-level sensor. For any detection protocol, the precision achieved depends on the signal's frequency and can be quantified by the quantum Fisher information. To study limitations in broadband sensing, we introduce the integrated quantum Fisher information and derive inequality bounds that embody fundamental tradeoffs in any sensing protocol. These inequalities show that sensitivity in one frequency range must come at a cost of reduced sensitivity elsewhere. For many protocols, including those with small phase accumulation and those consisting of $\pi$-pulses, we find the integrated Fisher information scales linearly with $T$. We also find protocols with substantial phase accumulation can have integrated QFI that grows quadratically with $T$, which is optimal. These protocols may allow the very rapid detection of a signal with unknown frequency over a very wide bandwidth.