  We address estimation of the minimum length arising from gravitational
theories. In particular, we provide bounds on precision and assess the use of
quantum probes to enhance the estimation performances. At first, we review the
concept of minimum length and show how it induces a perturbative term appearing
in the Hamiltonian of any quantum system, which is proportional to a parameter
depending on the minimum length. We then systematically study the effects of
this perturbation on different state preparations for several 1-dimensional
systems, and we evaluate the Quantum Fisher Information in order to find the
ultimate bounds to the precision of any estimation procedure. Eventually, we
investigate the role of dimensionality by analysing the use of two-dimensional
square well and harmonic oscillator systems to probe the minimal length. Our
results show that quantum probes are convenient resources, providing potential
enhancement in precision. Additionally, our results provide a set of guidelines
to design possible future experiments to detect minimal length.
