oton "is" in any of these quantum states. Next, I introduce two other components: the half-wave plate (HWP) and the polarization beamsplitter (PBS). As its name indicates, the HWP is similar to the previously described QWP, except that the net phase delay experienced by two orthogonal E-field components is now IT or one half of a wavelength. As in the QWP case, the fast axis of the plate must be oriented at 45° of the incident E-field polarization direction, assumed linear. Since the phase shift corresponds to a factor eir = the sign of one of the two polarization components is reversed, and the result is a 90° rotation of the incident linear polarization. Thus, the HWP swaps the basis states {1, into each other, which is equivalent the transformations |0) |1) and |1) |0), corresponding to the action of the Pauli matrix X on the states [0), ] |1) (see Chapter 16). If the incident E-field polarization is circular, the HWP axis orientation is unchanged, but the direction of rotation is reversed. Thus, the effect of the HWP is to swap the basis states {n, U} into each other, which is equivalent to the transformations 1+) |-) and |-) I+), corresponding to the action of the Pauli matrix Z on the states |+), |-) (see Chapter 16). Thus, placing HWP next to a linearly polarized SP source and orienting it at either 0° or 45° makes it possible to generate single photons into either the |0) or the |1) linear-polarization state. The PBS is a special assembly of birefringent crystal prisms whose effect, as the name indicates, is to separate an incident light beam into two orthogonally polarized components. As shown in Fig. 25.5, a detector SPD1 placed in the straight-through path only detects vertically polarized, or |0) photons, while a detector SPD2 placed in the "reflection" path only detects horizontally polarized, or |1) photons. The PBS-SPD1- SPD2 set-up, thus, constitutes a quantum measurement apparatus to determine the state of linearly polarized photons. If a count is obtained from SPD1 or from SPD2, we may attribute