Probing deformed quantum commutators

Understand

Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning.

• In quantum mechanics, the insurgence of such minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on the position measurement has a lower bound.
• The value of the minimal length is not predicted by theories and must be evaluated experimentally.
• In this paper, we address the quantum bound to estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra of the Hilbert subspace.