  The notion of perfect correlations between arbitrary observables, or more
generally arbitrary POVMs, is introduced in the standard formulation of quantum
mechanics, and characterized by several well-established statistical
conditions. The transitivity of perfect correlations is proved to generally
hold, and applied to a simple articulation for the failure of Hardy's
nonlocality proof for maximally entangled states. The notion of perfect
correlations between observables and POVMs is used for defining the notion of a
precise measurement of a given observable in a given state. A longstanding
misconception on the correlation made by the measuring interaction is resolved
in the light of the new theory of quantum perfect correlations.
