Abstract
A total set of n states |i〉 and the corresponding projectors Π(i)=|i〉〈i| are considered, in a quantum system with d-dimensional Hilbert space H(d). A partially known density matrix ρ with given p(i)=Tr[ρΠ(i)] (where i=1,…,n and d≤n≤d2−1) is considered, and its ranking permutation is defined. It is used to calculate the Choquet integral C(ρ) which is a positive semi-definite Hermitian matrix. Comonotonicity is an important concept in the formalism, which is used to formalize the vague concept of physically similar density matrices. It is shown that C(ρ)∕Tr[C(ρ)] is a density matrix which is a good approximation to the partially known density matrix ρ.
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