  The Haagerup approximation property for a von Neumann algebra equipped with a
faithful normal state $\varphi$ is shown to imply existence of unital,
$\varphi$-preserving and KMS-symmetric approximating maps. This is used to
obtain a characterisation of the Haagerup approximation property via quantum
Markov semigroups (extending the tracial case result due to Jolissaint and
Martin) and further via quantum Dirichlet forms.
