lities, this leads to the following property (as is easily mentally checked): (18.18) This result shows that any measurement Eim of the EPR-Bell states has a 50% chance of successfully projecting into any of the pure states. The 16 possible measurements resulting in the corresponding state collapses (phase factors e-ir/2 being omitted) are summarized in Table 18.1. As expected, we observe from the table that the EPR-Bell states collapse into any of the pure states |00), |01), |10), |11). We see that using a positive measurement E1m necessarily collapses the EPR-Bell pair into the pure state |m) X /x), and a positive measurement E2m necessarily collapses the EPR-Bell pair into the pure state /x) X |m), where X = 0, 1. This has the consequence that regardless of the four possible EPR-Bell pairs, a single positive measurement yields absolute information on one of the two qubits in the collapsed state. Because the first measurement gives only one qubit information, a second measure- ment would be necessary to get the missing information concerning the other qubit. But we do not need to make a second measurement if we know in advance the initial EPR-Bell pair. Indeed, Table 18.1 illustrates that the advance knowledge of 1Boo), 1001), |B10), 1B11) Qubit measurements, coding, and teleportation Table 18.1 State collapses resulting from single-qubit measurements Ein on the EPR-Bell states 1Boo), 1001), 1B10), 1B11). |Boo> |Bo1) 1B10) 1B11) Alice Measures Collapse Measures Figure 18.4 Two successive measurements by Alice then Bob in an entangled quantum state, here 1B01). and the choice of a single-measurement operator E10, E11, E20, E21 absolutely defines the collapsed state and, hence, the value of the two entangled qubits. For instance, if we use |B11), the single measurement E21 yields the 2-qubit |01) = |0) X |1) and the absolute information therein. Thus, given the knowledge of the system EPR-Bell pair, any positive measurement of one of the two qubits conditions the information knowledge of the other qubit. Because 