The quantum Cramér–Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We experimentally demonstrate near saturation of the quantum Cramér–Rao bound in the phase estimation of a solid-state spin system, provided by a nitrogen-vacancy center in diamond. This is achieved by comparing the experimental uncertainty in phase estimation with an independent measurement of the related quantum Fisher information. The latter is independently extracted from coherent dynamical responses of the system under weak parametric modulations, without performing any quantum-state tomography. While optimal parameter estimation has already been observed for quantum devices involving a limited number of degrees of freedom, our method offers a versatile and powerful experimental tool to explore the Cramér–Rao bound and the quantum Fisher information in systems of higher complexity, as relevant for quantum technologies.

量子Cramér-Rao界对量子系统中无偏参数估计的准确性设置了基本限制，将确定参数的不确定性与量子Fisher信息的倒数联系起来。我们通过实验证明了由金刚石中的氮空位中心提供的固态自旋系统的相位估计中量子Cramér-Rao 的接近饱和。这是通过将相位估计中的实验不确定性与相关量子费舍尔信息的独立测量进行比较来实现的。后者是从系统在弱参数调制下的相干动态响应中独立提取的，无需执行任何量子态断层扫描。