The generalization of probability distributions on density matrices allows to define quantum Jensen–Shannon divergence (QJSD), which uses von Neumann entropy. Does QJSD appear in any quantum algorithms or texts on quantum computing?
That quantity appears to be identical to Holevo information, which turns out to be the upper bound on how much classical information you can transmit using a quantum channel .
More generally the Holevo information is an upper bound for a quantity called "accessible information" which is (roughly speaking) the maximum information you can learn from an optimal measurement performed on an ensemble of quantum states.
 Holevo, A. S. (1973). Bounds for the quantity of information transmitted by a quantum communication channel. Problemy Peredachi Informatsii, 9(3), 3-11.