GROUND STATE EUCLIDEAN MEASURES FOR QUANTUM LATTICE SYSTEMS ON COMPACT MANIFOLDS

For pairs(omega),(rho) of density operators on a finite-dimensional Hilbert space of dimension d I call k-fidelity the d- k smallest eigenvalues of |((SQRT)(omega)) ((SQRT)(rho))| . Representations of k-fidelities are given showing their joint concavity in (omega), (rho) . For k = 0 the known properties of fidelities and transition probabilities are reproduced. Partial fidelities characterize equivalence classes of pairs of density operators which are partially ordered in a natural way.