Let $\mathbf{Z}$ be a $m\times n$ matrix with zero-mean unit-variance i.i.d complex Gaussian entries. What is the maximum value of mutual information $I(\mathbf{X}_1,\mathbf{X}_2;\mathbf{Y})$ such that \begin{align} \mathbf{Y}=\mathbf{X}_1^\mathrm{H}\mathbf{X}_2+\mathbf{X}_1^\mathrm{H}\mathbf{Z}, \end{align} where $\mathbf{X}_1$ and $\mathbf{X}_2$ are two $m\times n$ arbitrary random matrices and $(.)^\mathrm{H}$ denotes hermitian of matrix.

Let $\mathbf{Z}$ be a $m\times n$ matrix with zero-mean unit-variance i.i.d complex Gaussian entries. What is the maximum value of mutual information $I(\mathbf{X}_1,\mathbf{X}_2;\mathbf{Y})$ such that \begin{align} \mathbf{Y}=\mathbf{X}_1^\mathrm{H}\mathbf{X}_2+\mathbf{X}_1^\mathrm{H}\mathbf{Z}, \end{align} where $\mathbf{X}_1$ and $\mathbf{X}_2$ are two $m\times n$ arbitrary random matrices and $(.)^\mathrm{H}$ denotes hermitian of matrix. Moreover, the column norm of $\mathbf{X}_i$'s are less than or equal to one.