Nonlinear Maccone-Pati Uncertainty Principle

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