Entanglement detection is one of the important topics in quantum information theory. Wootters formula can be seen as a high level criterion for entanglement detection or entanglement quantification. However, it is restricted to two-qubit system, and its generalization is also limited. Based on a thorough study of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state mixed with a W state and white noise, we find a connection between Wootters formula and the matched entanglement witness. Further study shows that for a four-qubit GHZ state mixed with a Dicke state and white noise, there is a new kind of Wootters formula.

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我们可以从精确的纠缠见证中得到什么标准？

纠缠检测是量子信息论的重要课题之一。Wootters 公式可以看作是纠缠检测或纠缠量化的高级标准。然而，它仅限于二量子位系统，其泛化也受到限制。基于对混合了 W 态和白噪声的三量子比特 Greenberger-Horne-Zeilinger (GHZ) 态的深入研究，我们发现了 Wootters 公式与匹配的纠缠见证之间的联系。进一步的研究表明，对于混合了 Dicke 态和白噪声的四量子比特 GHZ 态，存在一种新的 Wootters 公式。