Quantum states of light can enable sensing configurations with sensitivities beyond the shot-noise limit. In order to better take advantage of available quantum resources and obtain the maximum possible sensitivity, it is necessary to determine fundamental sensitivity limits for different possible configurations for a given sensing system. Here, due to their wide applicability, we focus on optical resonance sensors, which detect a change in a parameter of interest through a resonance shift. We compare their fundamental sensitivity limits set by the quantum Cramr–Rao bound (QCRB) based on the estimation of changes in transmission or phase of a probing bright two-mode squeezed state (bTMSS) of light. We show that the fundamental sensitivity results from an interplay between the QCRB and the transfer function of the system. As a result, for a resonance sensor with a Lorentzian lineshape a phase-based scheme outperforms a transmission-based one for most of the parameter space; however, this is not the case for lineshapes with steeper slopes, such as higher order Butterworth lineshapes. Furthermore, such an interplay results in conditions under which the phase-based scheme provides a higher sensitivity but a smaller degree of quantum enhancement than the transmission-based scheme. We also study the effect of losses external to the sensor on the degree of quantum enhancement and show that for certain conditions, probing with a classical state can provide a higher sensitivity than probing with a bTMSS. Finally, we discuss detection schemes, namely optimized intensity-difference and optimized homodyne detection, that can achieve the fundamental sensitivity limits even in the presence of external losses.

光的量子态可以实现灵敏度超出散粒噪声限制的传感配置。为了更好地利用可用的量子资源并获得最大可能的灵敏度，有必要为给定的传感系统确定不同可能配置的基本灵敏度极限。在这里，由于它们的广泛适用性，我们专注于光学共振传感器，它通过共振位移检测感兴趣参数的变化。我们基于对光的探测明亮双模压缩状态 (bTMSS) 的透射或相位变化的估计，比较了由量子 Cramr-Rao 界 (QCRB) 设置的基本灵敏度限制。我们表明，基本灵敏度源于 QCRB 和系统传递函数之间的相互作用。其结果，对于具有洛伦兹线形的谐振传感器，对于大部分参数空间，基于相位的方案优于基于传输的方案；然而，对于具有更陡峭斜率的线形，例如高阶巴特沃斯线形，情况并非如此。此外，这种相互作用导致基于相位的方案比基于传输的方案提供更高的灵敏度但量子增强程度更小的条件。我们还研究了传感器外部损耗对量子增强程度的影响，并表明在某些条件下，用经典状态探测可以提供比用 bTMSS 探测更高的灵敏度。最后，我们讨论检测方案，即优化的强度差和优化的零差检测，