On diagonal N-representablity problem II: Sufficient conditions

Abstract

A set of transformational matrices (TM) is introduced which convert the weights of a mixed state into the diagonal elements of reduced density matrix (RDM). The formulae for the products of TM are deduced; the singular values of TM are calculated and the corresponding spectral expansion is built. The result of ambiguous reverse transformation of RDM diagonal elements is found. The conditions of nonnegativity of the reversed vector of the same dimension as the weight vector are established and shown to be coinciding in the case of the second RDM with the known necessary P-, G-, and Q-conditions of diagonal N-representability. The proper generalization to RDM of any order is given. It is demonstrated that the number of independent sufficient N-representability conditions coincides with the number of equations defining the diagonal RDM elements.