## Limiting Eigenvalue Distribution of Random Matrices Involving Tensor Product

Leonid Pastur

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

April 16, 2014

We consider two classes of \(n \times n\) sample covariance matrices arising in quantum informatics. The first class consists of matrices whose data matrix has \(m\) independent columns each of which is the tensor product of \(k\) independent \(d\)-dimensional vectors, thus \(n=d^k\). The matrices of the second class belong to \(\mathcal{M}_n(\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_2}), \ n=d_1 d_2\) and are obtained from the standard sample covariance matrices by the partial transposition in \(\mathbb{C}^{d_2}\).