  In this paper, we investigate the classicality and quantumness of a quantum
ensemble. We define a quantity called classicality to characterize how
classical a quantum ensemble is. An ensemble of commuting states that can be
manipulated classically has a unit classicality, while a general ensemble has a
classicality less than 1. We also study how quantum an ensemble is by defining
a related quantity called quantumness. We find that the classicality of an
ensemble is closely related to how perfectly the ensemble can be cloned, and
that the quantumness of an ensemble is essentially responsible for the security
of quantum key distribution(QKD) protocols using that ensemble. Furthermore, we
show that the quantumness of an ensemble used in a QKD protocol is exactly the
attainable lower bound of the error rate in the sifted key.
