AI 中文总结
研究非高斯量子态，定义由高阶正交单项式构建的高阶协方差矩阵，用于评估高斯变换对非高斯态的影响，可处理非线性压缩等问题，能从有限正交角零差测量数据估计，维度与模式数呈多项式缩放。
AI 中文摘要
协方差矩阵是描述连续变量高斯量子态的强大且成熟的辛框架的核心。然而，由于该框架仅依赖一阶和二阶矩，对于非高斯态分析不足，因其高阶矩对捕捉关键性质至关重要。本文定义高阶协方差矩阵，即由高阶正交单项式构建的协方差矩阵，它能评估高斯变换对非高斯态的影响，可用于处理非线性压缩或非高斯零化子等。高阶协方差矩阵可从仅使用有限数量正交角的零差测量数据估计，与福克基下的全模拟相比，涉及的矩阵维度适中，其维度不依赖于福克基下量子态的跨度，且仅与模式数呈多项式缩放。
英文摘要
Covariance matrices lie at the heart of the powerful and well-established symplectic framework for describing continuous-variable Gaussian quantum states. However, since this framework only relies on first- and second-order moments, it is not sufficient for the analysis of non-Gaussian states because their higher-order moments are essential to capture some of their key properties. Here, we define higher-order covariance matrices -- more precisely, covariance matrices built from higher-order quadrature monomials -- which provide a simple way to evaluate the effect of Gaussian transformations on non-Gaussian states and can be used, for example, to address nonlinear squeezing or non-Gaussian nullifiers. Higher-order covariance matrices can be estimated from homodyne measurement data using only a limited number of quadrature angles, which involves matrices of moderate dimension compared with a full simulation in the Fock basis. The dimension of a higher-order covariance matrix does not depend on the span of the quantum states in Fock basis and, furthermore, scales only polynomially with the number of modes.
Comments9 pages, 1 figure
