We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one correspondence with elements from the walled Brauer algebra. Using our formalism, these maps can be obtained in a systematic and clear way by manipulating partially transposed permutation operators under a partial trace. Additionally, these maps are reasonably easy in construction by combining an algorithmic approach with graphical calculus.

中文翻译：

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来自围墙布劳尔代数的正映射

我们提出正锥变量的正映射和矩阵不等式。这些不等式包含部分转置和重新洗牌操作，可以理解为正多线性映射，与围墙布劳尔代数中的元素一一对应。使用我们的形式主义，可以通过在部分迹下操作部分转置置换算子来以系统且清晰的方式获得这些映射。此外，通过将算法方法与图形微积分相结合，这些地图的构建相当容易。