sity operators PA, , to find: S(PA) = S(pB) = -2 X (1/2) log(1/2) = (21.71) Thus, each of the subsystems A, B has a quantum information equivalent to exactly one classical bit, which corresponds to the qubit state lq) = (|0) of maximal uncertainty. Such a conclusion is also consistent with our previous observation according to which the two subsystems A, B must be in mixed states (tr(p2) = tr(p) = = 1/2 < 1). The situation of the two subsystems, A, B, contrasts with that of the composite system, AB, which is in the pure state Boo). By definition, this state is known exactly and, therefore, it has zero quantum information, meaning that S(PAB) = 0. This is a most intriguing feature, without any counterpart in the classical world: there is no information in the composite system, while there is maximal information in the two subsystems! Formally, we obtain for the mutual information and the conditional entropy: S(PA;PB)=S(PA)+S(PB)-S(PAB) (21.72) =1+1-0=2, S(PA/PB) = S(PAB) S(PB) = 0 - 1 = -1 S(PB/PA) S(PAB) S(PA) = -1. (21.73) These results show that the two subsystems have the equivalent of two classical bits (two cbits) for mutual information, which shows that the 1-cbit information they each possess in fact constitute shared property! On the other hand, knowledge of the infor- mation contents of one subsystem removes one cbit from the information in the other subsystem, as the conditional entropy is negative. Since the other subsystem has one cbit of information content, there is actually no information left to measure! This obser- vation means that knowledge of one subsystem exactly conditions that of the other, which illustrates the principle of quantum entanglement. Another way to understand this conditioning property is to consider the effect of measuring the information in one of the two subsystems. Assume, for instance, that our measurement finds subsystem A in the state |0). The post-measurement state, which now characterizes subsystem B, is the pure state /VB) = |0) B. If our measurement finds subsystem A