标题： 非线性-线性对偶性用于多路径量子干涉 显示英文标题

标题： Nonlinear-linear duality for multipath quantum interference

摘要： 在量子光学中，非简并参量下转换（PDC）过程的后选择振幅通过部分时间反演与分束器（BS）相关联，除了与参量增益相关的归一化系数外[Proc. Natl. Acad. Sci. USA 117, 33107 (2020)]。增益较低的一个特殊例子类似于量子成像中的克利什科夫前波图像。在这里，我们提出并证明了一个广义的二象性，适用于多个空间路径连接由非简并PDC和线性光学系统组成的量子非线性干涉装置到一个线性装置的情况，其中PDC直接被假设的波长转换BS所替代。这种替换保持了原始装置的几何结构，级联的PDC变为光学腔，其计算涉及Redheffer星积。归一化系数中的附加项与腔内循环光子的贡献有关。然后，我们讨论了相干态输入和对$Q$函数计算的后选择情况。这个定理将在超越低增益极限的量子光子器件发展中有所帮助。 显示英文摘要

摘要： In quantum optics, the postselection amplitude of a nondegenerate parametric down-conversion (PDC) process is linked to a beamsplitter (BS) via partial time reversal, up to a normalization coefficient which is related to the parametric gain [Proc. Natl. Acad. Sci. USA 117, 33107 (2020)]. A special example where the gain is low is reminiscent of Klyshko's advanced-wave picture in quantum imaging. Here, we propose and prove a generalized duality for multiple spatial paths connecting a quantum nonlinear interference setup consisting of nondegenerate PDCs and linear optical systems to a linear one, where the PDCs are directly replaced by hypothetical wavelength-shifting BSs. This replacement preserves the geometry of the original setup, and cascaded PDCs become optical cavities whose calculation involves the Redheffer star product. Additional terms in the normalization coefficient are related to the contribution of looping photons inside the cavities. Then, we discuss the case of coherent state input and postselection for $Q$-function calculation. This theorem will be helpful in the development of quantum photonic devices beyond the low-gain limit.