The accessible information is the amount of classical information that can be extracted from a quantum system by an optimal measurement when the information is encoded using a particular ensemble of quantum states.
More precisely, consider an ensemble 
where the probabilities come from the random variable X. Let YP be the random variable that denotes the outcomes of the measurement described by a POVM P. The mutual information between X and Y
quantifies how much information Y contains about X. The accessible information is the maximum of this when all possible POVMs are possible,
Bounds
The accessible information is upper bounded by the Holevo quantity[1],
where S is the von Neumann entropy.
By substituting the von Neumann entropy in the Holevo quantity for the subentropy Q, one gets a lower bound [2],
References
[1] Information theoretical aspects of quantum measurements, Probl. Info.Transm. (USSR), vol. 9, no. 2, pp. 31–42, 1973 (in Russian); [translation: A. S. Kholevo,Probl. Info. Transm., vol. 9, pp. 177–183, 1973]
[2] Lower bound for accessible information in quantum mechanics, Richard Jozsa, Daniel Robb, and William K. Wootters, Publication Phys. Rev. A 49, 668 - 677 (1994)
