Ángel Rivas, Alfredo Luis
We develop practical schemes for the measurement of the covariance matrix for intrinsic angular-momentum variables in quantum optics. We particularize this approach to two-beam polarimetry and interferometry, as well as to ensembles of two-level atoms interacting with classical fields. We show the practical advantages of noisy simultaneous measurements.
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We investigate the separability of quantum states based on covariance matrices. Separability criteria are presented for multipartite states. The lower bound of concurrence proposed in Phys. Rev. A. 75, 052320 (2007) is improved by optimizing the local orthonormal observables.
Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in terms of covariance matrices have been derived. We show how these results can be used for the quantification of entanglement in bipartite systems. To that aim we introduce an entanglement parameter that quantifies the violation of the covariance matrix criterion and can be used to give a lower bounds on the concurrence. These lower bounds are easily computabl…
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。
Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.
To center or not to center? Hyperspectral data vs. quantum covariance matrices
本文研究了 $L^2$ 归一化对数据中心化的影响及其对量子幅度编码协方差矩阵的作用，发现只要妥善处理特征向量过滤，经主成分分析降维后的高光谱数据分类性能不受数据是否中心化的影响。
We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads to a family of sufficient conditions of inseparability based on the negativity of 2kth order inter-group covariance matrices of symmetric N-qubit systems. These conditions have a simple structure and detect entanglement in all even partitions of the symmetric multiqubit system. The observables involved are feasible experimental quantities and do not demand …
We present a criterion for multiparticle entanglement based on covariance matrices. On the one hand, the criterion allows to detect bound entangled states which are not detected by other criteria; on the other hand, some strongly entangled pure states such as the GHZ states are not detected. We show, however, that this is a general phenomenon: No separability criterion based on two-particle correlations can recognize the entanglement in the family of graph states, to which the GHZ states belong.
We derive steerability criteria applicable for both finite and infinite dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states particularly in high dimensional systems and that the Gaussian steering criteria for general M x N-modes of continuous variables are obtained as a special case. Extending from the approach of entanglement detection via covariance matrices, our criteria are based on the local uncertainty principles incorporating the asymmetric nature of steering scenario. Specifically,…
We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria -- such as the computable cross norm and local uncertainty criteria -- as well as their limitations.
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 …
A Result About the Classification of Quantum Covariance Matrices Based on Their Eigenspectra
针对连续变量量子系统协方差矩阵受不确定性原理约束的问题，本文找到了一类非平凡特征谱，证明其对应的量子协方差矩阵均可通过正交辛变换关联，且与识别高斯态热参数和压缩参数的非简并特征谱类重合。
Polar Duality and the Reconstruction of Quantum Covariance Matrices from Partial Data
本文利用拉格朗日与辛极对偶性解决量子协方差矩阵的重构问题，将其应用于高斯量子态以推广泡利重构问题，并给出了此类态的简单层析表征。
We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among qua…
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