It's a private company, with capitalist inversors (it's for profit) and all that... it's just that they do projects for the government.
The profit would not exist without government coercion and its request for services.
That's true, but whenever there's a private prison, the state is transfering part of their monopoly of violence (you have very limited rights as prisoner) to that private prison company. Therefore, as for the definition of state as monopoly of violence, you are breaking the state apart.
As i'm not an anarchist, I firmly believe in the state having the monopoly of violence (therefore existing).