Opportunities and Limitations in Broadband Sensing

Detecting a signal at an unknown frequency is a common task, arising in settings from dark-matter detection to magnetometry. For any detection protocol, the precision achieved depends on the frequency of the signal and can be quantified by the quantum Fisher information (QFI). To study limitations in broadband sensing, we introduce the integrated quantum Fisher information and derive inequality bounds that embody fundamental trade-offs in any sensing protocol. Our inequalities show that sensitivity in one frequency range must come at the cost of reduced sensitivity elsewhere.