On the covariance matrix for Gaussian states

Retrieving the Covariance Matrix of an Unknown Two-Mode Gaussian State by Means of a Reference Twin Beam

A method for revealing the covariance matrix of an unknown two-mode Gaussian state is given based on the interference with a reference twin beam whose covariance matrix is known. In the method, first- and second-order cross-correlation intensity moments are determined varying the overall phase of the reference twin beam.

纠缠量子态的双协方差模型：高斯约简到二阶协方差

Double Covariance Model for Entangled Quantum States: Gaussian Reduction to Second Order Covariances

该研究聚焦连接经典与量子物理概率形式体系中纠缠态经典概率生成问题，提出双协方差模型，利用高斯过程性质将其约简到二阶统计量，简化并推广了构造，阐明了并发度的经典概率意义。

用于非高斯量子态的高阶协方差矩阵

Higher-order covariance matrices for non-Gaussian quantum states

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。

Estimation of covariance matrix of macroscopic quantum states

For systems analogous to a linear harmonic oscillator, the simplest way to characterize the state is by a covariance matrix containing the symmetrically-ordered moments of operators analogous to position and momentum. We show that using Stokes-like detectors without direct access to either position or momentum, the estimation of the covariance matrix of a macroscopic signal is still possible using interference with a classical noisy and low-intensity reference. Such a detection technique will allow to estimate macroscopic quantum states of electromagnetic radiation without a coherent high-inte…

级联与局部耗散性实现线性量子系统以实现纯高斯态协方差分配

Cascade and locally dissipative realizations of linear quantum systems for pure Gaussian state covariance assignment

本文提出两种线性量子系统实现方法，用于纯高斯态协方差分配。级联实现通过构造级联量子系统生成指定协方差矩阵，局部耗散性实现则通过局部相互作用实现目标协方差矩阵。

Physical properties of the Schur complement of local covariance matrices

General properties of global covariance matrices representing bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a bipartite Gaussian state $ρ_{12}$ described by a $4\times 4$ covariance matrix \textbf{V}, the Schur complement of a local covariance submatrix $\textbf{V}_1$ of it can be interpreted as a new covariance matrix representing a Gaussian operator of party 1 conditioned to local parity measurements on party 2. The connection with a partial parity measurement over a bipartite quantum state and …