here (to recall) a, B are complex numbers satisfying |a|2 + 1812 = 1. It is clear that a, B represent the complex probability amplitudes of the qubit state, and that |a/2 or 1,812 represent the probabilities of the qubit being found in either pure state |0) or |1) of the base V. According to Eq. (18.3), the corresponding post-measurement states are (18.4) where eisa, eisp are unobservable phase factors, which can be omitted. Since the qubit is a superposition of states 1q) = a|0) + B|1), the action of any measurement in the state-base V, as defined by the operators M = |0) <01 or M1 = |1) (1), is, thus, to project, or collapse it into one of the two states |0) or |1). Using M, the probability that |q) collapses into |0) is p(0) = /a/2. Using M1, the probability that lq) collapses into |1) is p(1) = 1812 = 1 - /a/2. We can interpret the result of such a measurement as reducing the qubit information into the classical bit values 0 or 1, respectively. But unlike the classical case, there is no absolute certainty that the resulting information is, indeed, 0 or 1, when using measurement operators M0, M1, since either outcome is associated with some finite probabilities. For illustration, consider the following possibilities: (a) a = 0, B = 1, yielding p(0) = 0, p(1) = 1; (b) a = B = 1/2, yielding p(0) : p(1) = 1/2; (c) a = 1/3, B = 2/V3, yielding p(0) = 1/3, p(1) = 2/3; (d) a = 0.9, B= 0.1, yielding p(0) = 0.99, p(1) = 0.01. Qubit measurements, coding, and teleportation It is clear that in case (a), there is absolute certainty that the qubit measurement will result in the bit information 1. In case (b), the outcome has equal chances of being 0 or 1. In case (c) the odds on measuring 1 are twice those of measuring 0. In case (d), the odds are 99% for 0 and 1% for 1. It must be emphasized here that the above figures concern the measurement outcomes obtained by using the corresponding opera- tors M0, M1. Here comes a subtlety: in case (c), for instance, we know that we have a 1/3 chance of measuring 0 when using Mo. This