  Universal and complete graphical languages have been successfully designed
for pure state quantum mechanics, corresponding to linear maps between Hilbert
spaces, and mixed states quantum mechanics, corresponding to completely
positive superoperators. In this paper, we go one step further and present a
universal and complete graphical language for Hermiticity-preserving
superoperators. Such a language opens the possibility of diagrammatic
compositional investigations of antilinear transformations featured in various
physical situations, such as the Choi-Jamio{\l}kowski isomorphism, spin-flip,
or entanglement witnesses. Our construction relies on an extension of the
ZW-calculus exhibiting a normal form for Hermitian matrices.
