We study the problem of estimating the temperature of Gaussian systems with feasible measurements, namely Gaussian and photo-detection-like measurements. For Gaussian measurements, we develop a general method to identify the optimal measurement numerically, and derive the analytical solutions in some relevant cases. For a class of single-mode states that includes thermal ones, the optimal Gaussian measurement is either Heterodyne or Homodyne, depending on the temperature regime. This is in contrast to the general setting, in which a projective measurement in the eigenbasis of the Hamiltonian is optimal regardless of temperature. In the general multi-mode case, and unlike the general unrestricted scenario where joint measurements are not helpful for thermometry (nor for any parameter estimation task), it is open whether joint Gaussian measurements provide an advantage over local ones. We conjecture that they are not useful for thermal systems, supported by partial analytical and numerical evidence. We further show that Gaussian measurements become optimal in the limit of large temperatures, while {on/off} photo-detection-like measurements do it for when the temperature tends to zero. Our results therefore pave the way for effective thermometry of Gaussian quantum systems using $\textit{experimentally realizable measurements}$.

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使用高斯测量的高斯量子系统测温

我们研究了用可行的测量来估计高斯系统温度的问题，即高斯和类似光电探测的测量。对于高斯测量，我们开发了一种通用方法来数值识别最佳测量，并在某些相关情况下推导出解析解。对于包括热状态的一类单模状态，最佳高斯测量是外差或零差，具体取决于温度状态。这与一般设置相反，在一般设置中，无论温度如何，哈密顿量的本征基中的投影测量都是最佳的。在一般的多模式情况下，与联合测量对测温没有帮助（也对任何参数估计任务）没有帮助的一般不受限制的情况不同，联合高斯测量是否比局部测量具有优势是开放的。我们推测它们对热系统没有用，得到部分分析和数值证据的支持。我们进一步表明，高斯测量在高温极限下变得最佳，而 {on/off} 类似光电检测的测量在温度趋于零时做到这一点。因此，我们的结果为使用 $\textit{实验可实现测量}$ 的高斯量子系统的有效测温铺平了道路。而 {on/off} 类似光检测的测量在温度趋于零时进行。因此，我们的结果为使用 $\textit{实验可实现测量}$ 的高斯量子系统的有效测温铺平了道路。而 {on/off} 类似光检测的测量在温度趋于零时进行。因此，我们的结果为使用 $\textit{实验可实现测量}$ 的高斯量子系统的有效测温铺平了道路。