论文标题
两倍纠缠状态及其应用的非局部性的强度
Strength of the nonlocality of two-qubit entangled state and its applications
论文作者
论文摘要
非本地性是量子力学的特征，无法用局部现实理论解释。可以通过违反贝尔的不平等现象来检测到它。在这项工作中，我们在XOR游戏的帮助下考虑了对贝尔不平等的评估。在XOR游戏中，两个遥远的玩家之间共享了两个Qubit的纠缠状态。它可能会在玩家之间产生非本地相关性，这有助于最大的赢得比赛率。我们的目标是通过XOR游戏来确定非本地性的实力。因此，我们定义了一个数量$ s_ {nl} $，称为非本地性的强度，纯粹是基于赢得XOR游戏的最大概率。我们还得出了引入的数量$ s_ {nl} $与\ cite {horo3}中引入的数量$ m $之间的关系，以研究深度两倍的纠缠状态问题的非局部性。数量$ m $可以定义为给定纠缠状态的相关矩阵的两个最大特征值的总和，并确定在探测下给定的纠缠状态是否为非本地。此外，我们还探索了任何两量纠缠的状态的非局部性，CHSH不平等无法检测到其非局部性。有趣的是，当与$ CHSH $操作员对应的证人操作员无法检测到纠缠状态时，我们发现新定义的数量$ s_ {nl} $无法检测到纠缠状态的非局部性。为了克服这个问题，我们修改了非本地性强度的定义，并表明修改后的定义可以检测到此类纠缠状态的非局部性，而这些状态早些时候未被$ s_ {nl} $检测到。此外，我们还提供了强度$ s_ {nl} $的两种应用，以受控的量子传送和三个Qubit状态的非局部性到两个Qubit状态的非本地性。
Non-locality is a feature of quantum mechanics that cannot be explained by local realistic theory. It can be detected by the violation of Bell's inequality. In this work, we have considered the evaluation of Bell's inequality with the help of the XOR game. In the XOR game, a two-qubit entangled state is shared between the two distant players. It may generate a non-local correlation between the players which contributes to the maximum probability of winning of the game. We have aimed to determine the strength of the non-locality through XOR game. Thus, we have defined a quantity $S_{NL}$ called the strength of non-locality, purely on the basis of the maximum probability of winning of the XOR game. We have also derived the relation between the introduced quantity $S_{NL}$ and the quantity $M$ introduced in \cite{horo3}, to study the non-locality of a two-qubit entangled state problem in depth. The quantity $M$ may be defined as the sum of the two largest eigenvalues of the correlation matrix of the given entangled state and it determines whether the given entangled state under probe is non-local. Further, we have explored the non-locality of any two-qubit entangled state, whose non-locality cannot be detected by the CHSH inequality. Interestingly, we have found that the newly defined quantity $S_{NL}$ fails to detect non-locality for the entangled state, when the witness operator corresponding to $CHSH$ operator cannot detect the entangled state. To overcome this problem, we have modified the definition of the strength of non-locality and have shown that the modified definition may detect the non-locality of such entangled states, which were earlier undetected by $S_{NL}$. Furthermore, we have also provided two applications of the strength $S_{NL}$ of the non-locality in controlled quantum teleportation and linkage of non-locality of three qubit state to two-qubit state.
