Mutually exclusive uncertainty relations

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.