量子和亚波长成像的极限精度界
Ultimate precision bound of quantum and sub-wavelength imaging
摘要：
我们确定了量子成像的最终潜力，用于提高远场，衍射限制，线性成像设备内的近轴近似的分辨率。首先，我们证明了估计两个点状源之间的分离的问题等价于估计两个有损玻色子信道的损耗参数，即，两个分束器的透射率。利用这种表示，我们建立了在任意量子态中分辨两个点源的最终精度界，并对两个热源的具体情况给出了一个简单的公式。我们发现，根据标准的量子限制的精度范围与收集的光子数。然后，我们确定的源，其分离可以最佳估计，发现量子相关源（纠缠或不和谐）可以在亚瑞利尺度超分辨。我们的研究结果设定了任何现在或未来成像技术的上限，从天文观测到显微镜，这是基于量子探测以及源工程。
英文摘要：
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation between two point-like sources is equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Using this representation, we establish the ultimate precision bound for resolving two point-like sources in an arbitrary quantum state, with a simple formula for the specific case of two thermal sources. We find that the precision bound scales with the number of collected photons according to the standard quantum limit. Then we determine the sources whose separation can be estimated optimally, finding that quantum-correlated sources (entangled or discordant) can be super-resolved at the sub-Rayleigh scale. Our results set the upper bounds on any present or future imaging technology, from astronomical observation to microscopy, which is based on quantum detection as well as source engineering.
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