# Magnitude of off-diagonal terms in density matrix

I want to prove that if I have a density matrix of the form: $$\begin{pmatrix} p_{++}& p_{+-}\\ p_{-+}&p_{--} \end{pmatrix}$$

then $|p_{+-}|^2 = |p_{-+}|^2 \le p_{++}p_{--}$. (This was stated here). However, I don't know where to start. I appreciate if you could point the way to prove this. Thanks

Since density matrix is hermitian, $p_{+-}=p_{-+}^*$. As the eigenvalues are necessarily non-negative: $$\hbox{Det}\begin{pmatrix} p_{++}& p_{+-}\\ p_{-+}&p_{--} \end{pmatrix}= p_{++}p_{--}-\vert p_{+-}\vert^2 \ge 0$$ and the result follows.