Generalized Landau-Pollak Uncertainty Relation

TL;DR

This paper generalizes the Landau-Pollak uncertainty relation to include positive operator valued measures, providing a broader and more flexible bound applicable to multiple measures, advancing quantum measurement theory.

Contribution

It extends the Landau-Pollak uncertainty relation from rank one projections to positive operator valued measures, including a version for multiple measures.

Findings

Derived a generalized bound for pairs of positive operator valued measures

Presented a weak inequality applicable to multiple measures

Expanded the theoretical framework of quantum measurement uncertainty

Abstract

The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a generalization of this bound (weak version of the Landau-Pollak uncertainty relation). Our generalization covers a pair of positive operator valued measures. A nontrivial but slightly weak inequality that can treat an arbitrary number of positive operator valued measures is also presented.