Mutually exclusive uncertainty relations

TL;DR

This paper explores the role of mutually exclusive states in quantum uncertainty relations, generalizing and tightening bounds to better reflect incompatibility and exclusiveness among observables.

Contribution

It introduces generalized weighted uncertainty relations in product form and multi-observable cases, incorporating mutual exclusiveness to improve bound tightness.

Findings

New bounds are tighter than existing ones.

The relations capture both incompatibility and mutual exclusiveness.

Generalizations include product form and multi-observable analogues.

Abstract

The uncertainty principle is one of the characteristic properties of quantum theory based on incompatibility. Apart from the incompatible relation of quantum states, mutually exclusiveness is another remarkable phenomenon in the information-theoretic foundation of quantum theory. We investigate the role of mutual exclusive physical states in the recent work of stronger uncertainty relations for all incompatible observables by Mccone and Pati and generalize the weighted uncertainty relation to the product form as well as their multi-observable analogues. The new bounds capture both incompatibility and mutually exclusiveness, and are tighter compared with the existing bounds.