Coherence of Quantum Ensemble as a Dual to Uncertainty for a Single Observable

Abstract

The coherence of an ensemble of quantum states is considered — a quantity having a similarity with the uncertainty of the quantum observable that arises from the entropic uncertainty relations. We give estimates for the coherence of the ensemble through the uncertainty of the dual observable and the weak uncertainty of the observable through the coherence of the ensemble. It is shown that this numerical characteristic is closely connected with the relative entropy of discord for the corresponding classical-quantum state.