Mutually Exclusive Uncertainty Relations

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.

A Stronger Multi-observable Uncertainty Relation

“…Recently, some three observables uncertainty relations were studied, such as Heisenberg uncertainty relation for three canonical observables 25 , uncertainty relations for three angular momentum components 26 , uncertainty relation for three arbitrary observables 14 . Furthermore, some multiple observables uncertainty relations were proposed, which include multi-observable uncertainty relation in product 27 28 and sum 29 30 form of variances. It is worth noting that Chen and Fei derived an variance-based uncertainty relation 30 …”

Tighter uncertainty relations based on Wigner-Yanase skew information for observables and channels

“…Uncertainty relations for general multiple observables have been further studied either in product form [30,31] or sum form of variances [32][33][34][35][36].…”

Experimental investigation of multi-observable uncertainty relations

“…The generalization and improvement mainly focused on the uncertainty relation capable of dealing with more than two incompatible observables, i.e., the Heisenberg-type uncertainty relation for three canonical observables [27], uncertainty relations for angular momentum [28], and arbitrary incompatible observables [17]. There are also uncertainty relations with even more incompatible observables formulated in products [29,30] or sums [31][32][33] of variances.…”