Lower bound for accessible information in quantum mechanics

It has long been known that the von Neumann entropy S is an upper bound on the information one can extract from a quantum system in an unknown pure state. In this paper we define the ``subentropy'' Q, which we prove to be a lower bound on this information. Moreover, just as the von Neumann entropy is the best upper bound that depends only on the density matrix, we show that Q is the best lower bound that depends only on the density matrix. Other parallels between S and Q are also demonstrated.