I've been reading this paper about quantum fidelity estimation, but really have no idea what's going on when it comes to density matrix notation. In the abstract, they have the following quote:
provided that the purifications of ρ and σ are prepared by quantum oracles.
Where $\rho$ and $\sigma$ are the two mixed quantum states.
But I'm not really sure how these states are meant to be given. It says that they are "quantum oracles" but oracles must be unitary, wheras density matrices are Hermitian. So how are these states given?