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We introduce an axiomatic approach for characterizing quantum conditionalentropy. Our approach relies on two physically motivated axioms: monotonicityunder conditional majorization and additivity. We show that these two axiomsprovide sufficient structure that enable us to derive several key propertiesapplicable to all quantum conditional entropies studied in the literature.Specifically, we prove that any quantum conditional entropy must be negative oncertain entangled states and must equal -log(d) on dxd maximally entangledstates. We also prove the non-negativity of conditional entropy on separablestates, and we provide a generic definition for the dual of a quantumconditional entropy. Finally, we develop an operational approach forcharacterizing quantum conditional entropy via games of chance, and we showthat, for the classical case, this complementary approach yields the sameordering as the axiomatic approach.

Quantum conditional entropy from information-theoretic principles