On “partial” fidelities

For pairs ω, ρ of density operators on a finite-dimensional Hilbert space of dimension d I call k-fidelity the d − k smallest eigenvalues of ¦√ω√ρ¦. Representations of k-fidelities are given showing their joint concavity in ω, ρ. 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.