The spectral order for density operators is given in this paper Coecke Martin 2010. I won't give the full definition here. Essentially, it allows for a partial order of density matrices that forms a domain. What I am wondering is whether or not we can use it to define a monad on density operators that maps the set of density operators, $\Omega^n$, on a Hilbert space $\mathcal{H}^n$ to the set of domains on those density operators. I really have no idea how to do this. Any thoughts would be greatly appreciated.
Even if we can just define the functor, without the monad axioms, that would be helpful.
