Nonlinear Maccone-Pati Uncertainty Principle

Abstract

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of ${\mathcal{L}}^p$ spaces for $1<p<\infty$. Our main tool is the Clarkson inequalities. We also derive a nonlinear uncertainty principle for weak parallelogram spaces and Type-p Banach spaces.

6 pages, 0 figures