It has long been known that the von Neumann entropy S is an upper boun
d on the information one can extract from a quantum system in an unkno
wn 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 v
on Neumann entropy is the best upper bound that depends only on the de
nsity 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 demon
strated.