论文标题
基于重新调整操作的两个Quibit和双Qudit系统的一些纠缠标准
A few entanglement criterion for two-qubit and two-qudit system based on realignment operation
论文作者
论文摘要
众所周知，重新调整crierion是必要的，但对于较低和更高的尺寸系统而言不是足够的标准。在这项工作中，我们首先考虑一个两分的系统，并基于特定类别的两量子系统的重组操作得出了必要和充分的条件。因此，我们解决了是否且仅当针对特定的两分四分位状态部分条件的问题。我们已经表明，派生的必要条件检测到两个Qubit的纠缠状态，这些状态未通过重组标准检测到。接下来，我们讨论较高的维度系统，并获得了$ d \ otimes d $可分离状态的重新调整矩阵的最小奇异值的必要条件。此外，我们提供了$ d \ otimes d $ dimensional System的派生可分离性标准的几何解释。此外，我们表明我们的标准也可以检测到绑定的纠缠状态。从此处研究的纠缠检测标准是有益的，因为它只需要计算重新调整矩阵的最小值奇异值，而另一方面，重新调整标准需要重新调整矩阵的所有单数值。因此，我们的标准比重组标准具有计算优势。
It is known that realignment crierion is necessary but not a sufficient criterion for lower as well as higher dimensional system. In this work, we first consider a two-qubit system and derived the necessary and sufficient condition based on realignment operation for a particular class of two-qubit system. Thus we solved the problem of if and only if condition partially for a particular class of two-qubit state. We have shown that the derived necessary and sufficient condition detects two-qubit entangled states, which are not detected by the realignment criterion. Next, we discuss the higher dimensional system and obtained the necessary condition on the minimum singular value of the realigned matrix of $d\otimes d$ dimensional separable states. Moreover, we provide the geometrical interpretation of the derived separability criterion for $d\otimes d$ dimensional system. Furthermore, we show that our criterion may also detect bound entangled state. The entanglement detection criterion studied here is beneficial in the sense that it requires to calculate only minimum singular value of the realigned matrix while on the other hand realignment criterion requires all singular values of the realigned matrix. Thus, our criterion has computational advantage over the realignment criterion.
