  Quantum uncertainty is a well-known property of quantum mechanics that states
the impossibility of predicting measurement outcomes of multiple incompatible
observables simultaneously. In contrast, the uncertainty in the classical
domain comes from the lack of information about the exact state of the system.
One may naturally ask, whether the quantum uncertainty is indeed a fully
intrinsic property of the quantum theory, or whether similarly to the classical
domain lack of knowledge about specific parts of the physical system might be
the source of this uncertainty. This question has been addressed in the
previous literature where the authors argue that in the entropic formulation of
the uncertainty principle that can be illustrated using the, so-called,
guessing games, indeed such lack of information has a significant contribution
to the arising quantum uncertainty. Here we investigate this issue
experimentally by implementing the corresponding two-dimensional and
three-dimensional guessing games. Our results confirm that within the
guessing-game framework, the quantum uncertainty to a large extent relies on
the fact that quantum information determining the key properties of the game is
stored in the degrees of freedom that remain inaccessible to the guessing
party. Moreover, we offer an experimentally compact method to construct the
high-dimensional Fourier gate which is a major building block for various tasks
in quantum computation, quantum communication, and quantum metrology.
