  We discuss a combination of unitary and anti-unitary symmetry of quantum
Liouvillian dynamics, in the context of open quantum systems, which implies a
D2 symmetry of the complex Liovillean spectrum. For sufficiently weak
system-bath coupling it implies a uniform decay rate for all coherences, i.e.
off-diagonal elements of the system's density matrix taken in the eigenbasis of
the Hamiltonian. As an example we discuss symmetrically boundary driven open
XXZ spin 1/2 chains.
