Uncertainty relations for characteristic functions
Quantum Physics
2016-02-17 v3
Abstract
We present the uncertainty relation for the characteristic functions (ChUR) of the quantum mechanical position and momentum probability distributions. This inequality is more general than the Heisenberg Uncertainty Relation, and is saturated in two extremal cases for wavefunctions described by periodic Dirac combs. We further discuss a broad spectrum of applications of the ChUR, in particular, we constrain quantum optical measurements involving general detection apertures and provide the uncertainty relation that is relevant for Loop Quantum Cosmology. A method to measure the characteristic function directly using an auxiliary qubit is also briefly discussed.
Keywords
Cite
@article{arxiv.1505.04638,
title = {Uncertainty relations for characteristic functions},
author = {Łukasz Rudnicki and Daniel S. Tasca and Stephen P. Walborn},
journal= {arXiv preprint arXiv:1505.04638},
year = {2016}
}