ИСТИНА

The coherence of an ensemble of quantum states is considered - a quantity having a similarity with the uncertainty of a single quantum observable that arises from the entropic uncertainty relations [1]. This quantity describes the “quantumness” of the ensemble and is zero for the ensembles with only classical randomness. Using the duality between quantum states and observables [2], 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. We show that this numerical characteristic is closely connected with the relative entropy of discord [3, 4] for the corresponding classical-quantum state. We also show that the coherence of ensemble and at least weak uncertainty of observable are necessary for quantum key distribution.