Mixture of multiple copies of maximally entangled states is quasi-pure

Employing the general BXOR operation and local state discrimination, the mixed state of the form \rho^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|\phi_{mn}><\phi_{mn}|)^{\otim es k} is proved to be quasi-pure, where $\{|\phi_{mn}>\}$ is the canonical set of mutually orthogonal maximally entangled states in $d\times d$. Therefore irreversibility does not occur in the process of distillation for this family of states. Also, the distillable entanglement is calculated explicitly.