; or If Alice uses Z for her first qubit measurement of 1Boo), she obtains equally likely eigenvalues +1 with corresponding post-measurement or collapsed states |0) or |1), and cbits bk = 0 or bk = 1, respectively. We note here that Alice's measurements of the first qubits of the EPR pair 1Boo result in the instant collapse of the state into one of the qubits, 1/4/1 = 1+), |-), |0), or |1), depending on the measurement type and its eigenvalue outcome. Such a collapse is instant indeed, as a result of the intriguing property of entangled states called nonlocality. This term is attached to any widely separated systems, which can- not be treated as behaving independently, regardless their physical separation. It is thought-provoking that the action of Alice (on her qubit) instantly affects the system (hence, Bob's qubit) without consideration of wave propagation subjected to the speed of light, C. As in quantum teleportation (Chapter 18), there is no violation of Einstein's theory of special relativity, according to which information cannot travel faster than C. The nonlocality of entangled states, which permits their instant collapse, does 23 To recall, the states |11 are given by the qubit superpositions Thus, and, hence, 1800) 25.12 The EPR protocol not violate such a principle, because actually no information is exchanged in the process. 24 Next comes the clever thing about the EPR protocol. Indeed, if Bob then performs a measurement on his remaining qubit (the post-measurement state) B, incidentally at random with the same basis choices as Alice's, there is absolute certainty that his eigenvalues or cbits (b') exactly match those of Alice's (bk), just as with the BB84 protocol. Over a public channel, Alice and Bob only need to compare the bases they used (namely the cbits ak, ak), and retain as valid only their secret cbits bk, b' corresponding to the matching cases ak = ak. The same conclusion applies should Bob perform his measurement before Alice, or even at the same time! Indeed, the outcome of their measur