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In the present paper I show how it is possible to derive the Hilbert spaceformulation of Quantum Mechanics from a comprehensive definition of "physicalexperiment" and assuming "experimental accessibility and simplicity" asspecified by five simple Postulates. This accomplishes the program presented inform of conjectures in the previous paper quant-ph/0506034. Pivotal roles areplayed by the "local observability principle", which reconciles the holism ofnonlocality with the reductionism of local observation, and by the postulatedexistence of "informationally complete observables" and of a "symmetricfaithful state". This last notion allows one to introduce an operationaldefinition for the real version of the "adjoint"--i. e. the transposition--fromwhich one can derive a real Hilbert-space structure via either theMackey-Kakutani or the Gelfand-Naimark-Segal constructions. Here I analyze indetail only the Gelfand-Naimark-Segal construction, which leads to a realHilbert space structure analogous to that of (classes of generally unbounded)selfadjoint operators in Quantum Mechanics. For finite dimensions, generaldimensionality theorems that can be derived from a local observabilityprinciple, allow us to represent the elements of the real Hilbert space asoperators over an underlying complex Hilbert space (see, however, a still openproblem at the end of the paper). The route for the present operationalaxiomatization was suggested by novel ideas originated from Quantum Tomography.

How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms