宽带传感的机遇与局限
Opportunities and Limitations in Broadband Sensing
摘要：
我们考虑估计耦合到两级传感器的单色AC信号的幅度。对于任何检测协议，所实现的精度取决于信号的频率，并且可以通过量子费舍尔信息来量化。为了研究宽带传感的局限性，我们引入了集成的量子费舍尔信息，并推导出不等式界，体现在任何传感协议的基本权衡。这些不等式表明，在一个频率范围内的灵敏度必须以其他地方的灵敏度降低为代价。对于许多协议，包括具有小相位积累的协议和由$π$脉冲组成的协议，我们发现集成的Fisher信息与$T$成线性比例。我们还发现具有大量相位累积的协议可以具有与$T$成二次增长的集成QFI，这是最佳的。这些协议可以允许在非常宽的带宽上非常快速地检测具有未知频率的信号。
英文摘要：
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 $π$-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.
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