We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by performing a partial transposition on the operators. The method is highly efficient and versatile in the sense that the set of measurement operators can be freely chosen, do not need to be complete, and there is no constraint on the commutation relations. The method is particularly suited for systems with higher dimensionality since the computations do not scale with the dimension of the Hilbert space rather they scale with the number of chosen observables which can always be kept small. We illustrate the approach by examining the entanglement between two spin ensembles, and show that it detects entanglement in a basis independent way.

中文翻译：

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任意一组运算符的协方差矩阵纠缠标准

我们使用协方差矩阵对任意一组可观察量进行纠缠检测。使用协方差矩阵和交换矩阵构建广义不确定关系，然后通过对算子进行部分转置来建立准则。该方法在测量算子集可以自由选择、不需要完整、对换向关系没有约束的意义上是高效和通用的。该方法特别适用于具有更高维数的系统，因为计算不随 Hilbert 空间的维数而缩放，而是随所选可观察量的数量而缩放，而这些可观察量始终保持较小。我们通过检查两个自旋系综之间的纠缠来说明该方法，