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We address the precision of the estimation procedures for 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 performance. At first, we review the concept of minimum length and how it induces a perturbative term appearing in the Hamiltonian of any quantum system, which itself is proportional to a parameter depending on the minimum length. We then systematically study the effects of this perturbation on different state preparations and for several one-dimensional systems, and evaluate the quantum Fisher information in order to find the ultimate bounds to precision. Eventually, we investigate the role of dimensionality by analyzing 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 …
American Physical Society
Publication date: 
11 Sep 2020

Alessandro Candeloro, Cristian Degli Esposti Boschi, Matteo GA Paris

Biblio References: 
Volume: 102 Issue: 5 Pages: 056012
Physical Review D