Probing deformed quantum commutators

Abstract

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.

updated refs. 8 pages, 5 figures

References in corpus (3)

• Beating the Standard Quantum Limit with Four Entangled Photons
• Universality of Quantum Gravity Corrections
• Optimal quantum estimation of loss in bosonic channels

Cited by in corpus (3)

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• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator