Family of Quantum Mutual Information and Interaction Information in Multiparty Quantum Systems

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.