  Characterizing information in a multiparty system is crucial but cumbersome.
We extend the notion of conditional mutual information to multiparty systems
and introduce a family of genuinely multiparty quantum mutual information. The
two versions of multiparty quantum mutual information known in the literature
are part of this family. We also conjecture them to qualify for secrecy
monotones useful in quantum cryptography. We give interpretations and discuss
their properties and some unresolved issues.
