tain number of interesting properties, and as we shall see further down, really "stunning" applications. As a first property, there exists no tensor product of pure states or of qubits that is capable of generating any of the EPR-Bell states. This is left as a straightforward exercise to check. Because the EPR-Bell states cannot be decomposed as a qubit tensor product, they are called entangled states. A faster way to realize the nature of entanglement is to observe that none of the states in Eq. (18.15) can be factorized into a pure-state product of the form |i>|j) = |0>|0), |0)|1), |1)|0), |1)|1). Thus, it is not possible to tell what the states of the first and the second qubits are. While the EPR-Bell states are not tensor products of qubit states, they can, however, be generated by means of quantum gates. The circuit shown in Fig. 18.3, which comprises a Hadamard gate and a CNOT gate (Chapter 16) represents one possibility for the generation of EPR-Bell states. As we saw in that earlier chapter, the Hadamard gate transforms the input qubit |0) into the mixed state 1+) = (|0) + |1))/2, and the input qubit |1) into the mixed state |-) = (|0) - |1))/2. Thus, for the quantum gate in Fig. 18.3, the tensor input |0) /yy results in (H|x)) = 0)+x=1))0xoy)/V2 = = (0)0)y)+|1)1)y))//2 (18.16) Hence, |0) |0) |0) X |1) -> (|0, + -|1,0))/ V2=|B01). The two other results for the inputs |1) Oly are also readily verified. 18.2 Measuring n-qubits Figure 18.3 Quantum circuit for the generation of EPR-Bell states |Bxy) as defined in Eq. (18.15). As a second property, the EPR-Bell states form an orthonormal basis for any 2-qubit |kl) and any superposition thereof. Indeed, it is straightforward to see from Eq. (18.15) (18.17) hence, any 2-qubit superposition of the above pure |ij) states accepts a unique decom- position over the EPR-Bell states. Third, we notice from the definitions in Eq. (18.5) that the EPR-Bell states represent a mix of2-qubits |ij) and |kl) satisfying i = 0, k = 1, and j, l = 0, 1. For the measurement probabi