Oh Changhun, Zhou Sisi, Wong Yat, Jiang Liang
Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA.
Department of Physics, Yale University, New Haven, Connecticut 06511, USA.
Phys Rev Lett. 2021 Mar 26;126(12):120502. doi: 10.1103/PhysRevLett.126.120502.
We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with noiseless cases where the quantum Fisher information has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution. In addition, we show that false excitation on an arbitrary measurement, such as dark counts, also makes the classical Fisher information of the measurement approach to zero as the separation goes to zero. Finally, a practically relevant situation resolving two identical thermal sources is quantitatively investigated by using the quantum and classical Fisher information of finite spatial mode multiplexing, showing that the amount of noise poses a limit on the resolution in a noisy system.
我们分析了在噪声环境中分辨两个相同源的最终量子极限。我们证明，在存在诸如热噪声等导致虚假激发的噪声情况下，用于量化物体分离分辨率的任意量子态的量子 Fisher 信息，随着分离趋于零，总是收敛到零。有噪声的情况与无噪声的情况形成对比，在无噪声情况下，已表明量子 Fisher 信息在各种情况下对于小距离是非零的，这揭示了超分辨率。此外，我们表明，诸如暗计数等任意测量上的虚假激发，也会使测量的经典 Fisher 信息随着分离趋于零而趋近于零。最后，通过使用有限空间模式复用的量子和经典 Fisher 信息，对分辨两个相同热源的实际相关情况进行了定量研究，结果表明噪声量对有噪声系统中的分辨率构成了限制。
