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A universal formulation of the quantum uncertainty regarding quantumindeterminacy, quantum measurement, and its inevitable observer effect ispresented with additional focus on the representability of quantum observablesover a given state. The operational tangibility of the framework assures thatthe resultant general relations admit natural operational interpretations andcharacterisations, and thereby perhaps most importantly, their experimentalverifiability. In view of the universal formulation, Heisenberg's originalphilosophy of the uncertainty principle, most typically exemplified in hisfamous gamma-ray microscope Gedankenexperiment, is revisited; it isreformulated and restated as a refined no-go theorem, albeit perhaps in aweaker form than was originally intended. The relations entail, in essence ascorollaries to their special cases, several previously known relations,including most notably the standard Kennard-Robertson relation, theArthurs-Kelly-Goodman relations for joint measurement as well as the Ozawa andthe Watanabe-Sagawa-Ueda relations for error and error-disturbance.

A Universal Formulation of Uncertainty Relation for Error-Disturbance and Local Representability of Quantum Observables