Continuous Krishna-Parthasarathy Entropic Uncertainty Principle

In 2002, Krishna and Parthasarathy [$\mathit{\text{Sankhy}}\overline{\mathit{\text{a}}}\mathit{\text{Ser.}}\mathit{\text{A}}$] derived discrete quantum version of Maassen-Uffink [$\mathit{\text{Phys.}}\mathit{\text{Rev.}}\mathit{\text{Lett.,}}\mathit{\text{1988}}$] entropic uncertainty principle. In this paper, using the notion of continuous operator-valued frames, we derive an entropic uncertainty principle for arbitrary family of operators indexed by measure spaces having finite measure. We give an application to the special case of compact groups.