The spectral order for density operators is given in this paper [Coecke Martin 2010](https://link.springer.com/chapter/10.1007/978-3-642-12821-9_10).  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.