Asymptotic Attainment for Quantum Relative Entropy

In this paper it was proved that the quantum relative entropy D(k) can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of measurements. The sequence of measurements depends on , but is independent of the choice of . In classical statistical theory the relative entropy D(pkq) is an information quantity which means the statistical eÆciency in order to distinguish a probability measure p of a measurable space from another probability measure q of the same measurable space. The states correspond to measures on measurable space. When p; q are discrete probabilities, the relative entropy (called also information divergence) introduced by Kullback and Leibler is dened by [1]: D(pkq) := X i p i log p i q i : In general, when p; q are measures on measurable space the relative entropy is dened by: D(pkq) := Z log dq dp (!)p( d!); where dq dp (!) is Radon-Nikodym derivative of q with respect to p. In this paper, we co..