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Based on a recent relational formulation of quantum reference frametransformations, especially with a case of quantum spatial translations inparticular, we analyzed how the `value' of an observable for a fixed statechange. That is the exact analog of the classical description, for example, ofthe value of the $x$-coordinate for a particle decrease by 2 units when weperform a translation of the reference frame putting the new origin at $x=2$.The essence of the quantum reference frame transformations is to have thequantum fluctuations, and even entanglement, of the physical object whichserves as the (new) reference frame, taken into account. We illustrate how therecently introduced notion of the noncommutative values of quantum observablesgives such a definite description successfully. Formulations, and an analysisof a case example in qubit systems, of analog transformations for observableswith a discrete or finite spectrum is also presented. Issues about the evolvingpicture of the symmetry system of all quantum reference frame transformationsdiscussed.

Quantum Frames of Reference and the Noncommutative Values of Observables