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We study the problem of separating the data produced by a given quantummeasurement (on states from a memoryless source which is unknown except for itsaverage state), described by a positive operator valued measure (POVM), into a"meaningful" (intrinsic) and a "not meaningful" (extrinsic) part. We are ableto give an asymptotically tight separation of this form, with the "intrinsic"data quantfied by the Holevo mutual information of a certain state ensembleassociated to the POVM and the source, in a model that can be viewed as theasymptotic version of the convex decomposition of POVMs into extremal ones.This result is applied to a similar separation therorem for quantum instrumentsand quantum operations, in their Kraus form. Finally we comment on links torelated subjects: we stress the difference between data and information (inparticular by pointing out that information typically is strictly less thandata), derive the Holevo bound from our main result, and look at its classicalcase: we show that this includes the solution to the problem ofextrinsic/intrinsic data separation with a known source, then compare with thewell-known notion of sufficient statistics. The result on decomposition ofquantum operations is used to exhibit a new aspect of the concept of entropyexchange of an open dynamics. An appendix collects several estimates for mixedstate fidelity and trace norm distance, that seem to be new, in particular aconstruction of canonical purification of mixed states that turns out to bevaluable to analyze their fidelity.Comment: 17 pages, 3 included eps figures, revtex4. v2: revised with a more  accessible introduction, and added references. Submitted. v3: part of  appendix A had to be deleted as it turned out to be wrong. Happily, though,  all other results remain unchange

??Extrinsic?? and ??Intrinsic?? Data in Quantum Measurements: Asymptotic Convex Decomposition of Positive Operator Valued Measures