论文标题
对任何内在矩阵及其排列的二次形式估算二次形式
Interferometrically estimating a quadratic form for any immanant of a matrix and its permutations
论文作者
论文摘要
我们设计了一个多速量干涉计量方案，用于对单位矩阵的任何子矩阵及其行排列进行比较内在的二次函数。完整的统一矩阵描述了一个被动的线性干涉仪，当光子进入并在可能的输入和输出通道的子集中检测到时，使用其子序列。内在的是数学结构，可以在永久性和决定因素之间插入。与具有有意义的物理应用的决定因素和永久物相反，内在人物在经典上没有物理意义，但在量子环境中被证明是有意义的。通过将真空和单个光子注入干涉仪输入端口，我们的二次内在形式可以采样，以使光子到达时间纠缠在一起，与以前控制到达时间而无需纠缠的方法相反。我们的方法适用于任意数量的光子，我们针对两，三片和四个光子的情况明确解决了二次形式。
We devise a multiphoton interferometry scheme for sampling a quadratic function of a specific immanant for any submatrix of a unitary matrix and its row permutations. The full unitary matrix describes a passive, linear interferometer, and its submatrix is used when photons enter in and are detected at subsets of possible input and output channels. Immanants are mathematical constructs that interpolate between the permanent and determinant; contrary to determinants and permanents, which have meaningful physical applications, immanants are devoid of physical meaning classically but here are shown to be meaningful in a quantum setting. Our quadratic form of immanants is sampled by injecting vacuum and single photons into interferometer input ports such that the photon arrival times are entangled, in contrast to previous methods that control arrival times without entangling. Our method works for any number of photons, and we solve explicitly the quadratic form for the two-, three- and four-photon cases.
