quantum mechanics - Can isotropic states have bound entanglement?

Let us consider the maximally entangled state

$$\begin{equation} |\psi\rangle=\frac{1}{\sqrt{n}}(|0,0\rangle+\cdots+|n-1,n-1\rangle) \end{equation}$$ and construct the pseudo-pure state $$\begin{equation} \rho_\lambda=(1-\lambda)|\psi\rangle\langle\psi|+\lambda\frac{I_{n^2}}{n^2}, \end{equation}$$ where $I_{n^2}$ is the identity matrix and $0\leq\lambda\leq1$. I was told that for any dimension $n$ and for any $\lambda$, $\rho_\lambda$ is either separable or entangled which can be determined by partial transpose. It can be rephrased as

There does not exists any dimension $n$ and any $\lambda$ such that the corresponding $\rho_\lambda$ is a bound entangled state.

I could not find out the proof and could not make one by myself. Can someone give me a proof or at least refer a paper containing the proof. Advanced thanks for any suggestion.

ADDITION: Also the same question can be asked for the case, when the coefficients of $|j,j\rangle$ are non-uniformly distributed nonzero complex numbers (such that the sum is $1$).