Von Neumann entropy in terms of the tangle

[barnflakes]

The Von Neumann entropy is \mathcal{S}(|\psi\rangle) = -Tr[\rho_a ln \rho a]. The linear entropy S_L = \frac{l}{l-1}(1 - Tr[\rho_a^2]) For l =2 the linear entropy is written 4Det(\rho_A) which is also called the tangle \tau. I understand this just fine, I can show that. Now it says the Von Neumann can be written:

\mathcal{S}(|\psi\rangle) = -xln_{2}x - (1-x)ln_{2}(1-x) where x = (1+\sqrt{1-\tau})/2

I don't know how to show this last step? Anyone offer any insight? This is for a 2-dimensional case if that isn't clear from the above.

 

[barnflakes]

Nobody know?