Remarks on the uncertainty relation in scattering theory

pO N Golubjeva, L A Minasyanp

David Pierre Ruelle

Romeo Brunetti, Klaus Fredenhagen

Dedicated to Huzihiro Araki on the occasion of his seventieth birthday Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation for time meaurements alone. 1

Yunlong Xiao, Naihuan Jing

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.