We study entanglement witnesses (EWs) and construct a linear map by taking two groups of mutually unbiased bases (MUBs) of two Hilbert spaces. We provide two new relations about matrices (may not be square matrices) with properties similar to unitary matrix. Using these two new relations, we obtain a positive map between two different linear spaces of complex matrices. Finally, we calculate a special case by applying our map to get an EW on \(\mathbb {C}^{3}\otimes \mathbb {C}^{4}\). We also find three entangled states detected by this EW.

中文翻译：

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从两个互不偏倚的基地构建纠缠证人

我们研究纠缠目击者（EWs）并通过采用两个希尔伯特空间的两组互不偏基（MUB）构造线性图。我们提供了有关矩阵（可能不是平方矩阵）的两个新关系，其性质类似于unit矩阵。使用这两个新关系，我们获得了两个不同的复杂矩阵线性空间之间的正图。最后，我们通过应用地图在\（\ mathbb {C} ^ {3} \ otimes \ mathbb {C} ^ {4} \）上获得EW来计算特殊情况。我们还发现此电子战检测到的三个纠缠状态。