Yuan Yuan, Huang Xufeng, Niu Yueping, Gong Shangqing
School of Physics, East China University of Science and Technology, Shanghai 200237, China.
Shanghai Engineering Research Center of Hierarchical Nanomaterials, Shanghai 200237, China.
Entropy (Basel). 2023 Oct 17;25(10):1459. doi: 10.3390/e25101459.
Quantum coherence is the most distinguished feature of quantum mechanics. As an important resource, it is widely applied to quantum information technologies, including quantum algorithms, quantum computation, quantum key distribution, and quantum metrology, so it is important to develop tools for efficient estimation of the coherence. Bell state measurement plays an important role in quantum information processing. In particular, it can also, as a two-copy collective measurement, directly measure the quantum coherence of an unknown quantum state in the experiment, and does not need any optimization procedures, feedback, or complex mathematical calculations. In this paper, we analyze the performance of estimating quantum coherence with Bell state measurement for a qubit case from the perspective of semiparametric estimation and single-parameter estimation. The numerical results show that Bell state measurement is the optimal measurement for estimating several frequently-used coherence quantifiers, and it has been demonstrated in the perspective of the quantum limit of semiparametric estimation and Fisher information.
量子相干是量子力学最显著的特征。作为一种重要资源，它被广泛应用于量子信息技术，包括量子算法、量子计算、量子密钥分发和量子计量学，因此开发高效估计相干性的工具很重要。贝尔态测量在量子信息处理中起着重要作用。特别是，它还可以作为一种双拷贝集体测量，在实验中直接测量未知量子态的量子相干性，并且不需要任何优化程序、反馈或复杂的数学计算。在本文中，我们从半参数估计和单参数估计的角度分析了在量子比特情形下用贝尔态测量估计量子相干性的性能。数值结果表明，贝尔态测量是估计几个常用相干性量化器的最优测量，并且已经从半参数估计的量子极限和费舍尔信息的角度得到了证明。
