On partial fidelities

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 \root omega root 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.