Quantum Generalizations of Multivariate Classical Fidelities

The authors introduce several quantum generalizations of multivariate classical fidelities, such as the average pairwise z-fidelity, multivariate semi-definite programming fidelity, secrecy-based multivariate fidelity, and multivariate log-Euclidean fidelity. These multivariate quantum fidelities satisfy desirable properties like reduction to classical multivariate fidelities for commuting states, data processing inequality, symmetry, faithfulness, orthogonality, direct-sum property, and joint concavity.