Relations among elements of the density matrix. I. Definiteness inequalities

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Abstract
The statistical operator of quantum theory may be determined empirically by computations based upon the measured mean values of a set of observables we have called a quorum. The requirement that a statistical operator be positive semidefinite is then used to generate a family of inequalities connecting these quorum means. Like the simpler uncertainty relations, these inequalities are universal, valid for all quantum states. In the special case of pure states, the method yields a family of equalities.