arXiv 1809.025442018-09quant-ph

多模压缩中的结构：一个推广的Bloch-Messiah约化

Structure in Multimode Squeezing: A Generalised Bloch-Messiah Reduction

Will McCutcheon

摘要：

分解非线性光学变换的方法因设置而异，导致用于模拟光子对源的处理与用于模拟简并下转换过程的处理相比存在明显差异。将高斯过程简化为单模压缩器和被动（线性）幺正，与将光子对源分解为双模压缩器和被动幺正的施密特分解的实用性并置。在这里，我们提出了一个通用的框架，统一这些形式，以及阐明更一般的结构，在多模高斯变换。分解是通过引入额外的约束到用于对角化高斯过程的布洛赫-弥赛亚减少，这些约束的物理约束的动机，从不同的物理自由度的不等价的系统，即。时间-光谱自由度与变换中的不同空间模式的关系。其结果是出现的双模压缩图片从减少，以及潜在的概括这些约束，以适应光谱缺陷的源产生3模式连续变量GHZ类状态。此外，我们考虑的实际情况下，变换的目的是产生一个多光子纠缠态，从而空间模式提供理想的自由度，而不希望的光谱模式结构贡献的噪声，并表明，这种光谱杂质可以有效地建模，找到一个最佳的低维基地，其模拟。

英文摘要：

Methods to decompose nonlinear optical transformation vary from setting to setting, leading to apparent differences in the treatments used to model photon pair sources, compared to those used to model degenerate down-conversion processes. The Bloch-Messiah reduction of Gaussian processes to single-mode squeezers and passive (linear) unitaries appears juxtaposed against the practicalities of the Schmidt-decomposition for photon pair sources into two-mode squeezers and passive unitaries. Here, we present a general framework which unifies these forms as well as elucidating more general structure in multimode Gaussian transformations. The decomposition is achieved by introducing additional constraints into the Bloch-Messiah reduction used to diagonalise Gaussian processes, these constraints motivated by physical constraints following from the inequivalence of different physical degrees of freedom in a system, ie. the temporal-spectral degrees of freedom vs different spatial modes in a transformation. The result is the emergence of the two-mode squeezing picture from the reduction, as well as the potential to generalise these constraints to accommodate spectral imperfections in a source generating 3-mode continuous variable GHZ-like states. Furthermore, we consider the practical scenario in which a transformation aims to generate a multiphoton entangled state, whereby spatial modes provide desirable degrees of freedom, whilst undesired spectral mode structure contributes noise, and show that this spectral impurity can be efficiently modeled by finding an optimal low dimensional bases for its simulation.

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