wo E-field components. It is then possible to express the resulting E-field in this basis as a vector with two complex coordinates Ekeiek, k = 1, 2 according to: (25.7) where W = 2V is the oscillation frequency in radian/s. In the case Q1 Q, we have from the above definition (25.8) Classical and quantum cryptography which corresponds to a time-invariant direction, (or oscillation plane) of the E-field. With the appropriate basis rotation (the choice being conventional), we may also write (25.9) which corresponds to a TE-polarized state. Such a representation is immediately rem- iniscent of a quantum state, namely here the qubit |0) from the basis {|0), |1)}. We may, thus, identify the TE polarization state with the quantum state |0). Consistently, we identify the TM polarization with the quantum state or qubit |1), but with an E-field relative phase to be determined later on. Consider next the case Q2 Let us rewrite Eq. (25.7) as (25.10) where we have overlooked the common phase factor ei(41+42)/2 Taking the real part of the E-field, we obtain: (25.11) The result in Eq. (25.11) shows that the two E-field components alternatively reach maxi- mal amplitudes at times t = 2n - 86/(2w) andt'=2nn + 86/(2w), respectively, with n being an integer. The E-field direction, thus, periodically rotates about the light ray axis at the frequency W = 2V Consider the special case 84 = /2, and for simplicity assume E1 = E2 = 1. From Eq. (25.11), and after basic trigonometry we obtain (within an arbitrary phase 4): (25.12) The result in Eq. (25.12) shows that the E-field periodically rotates about the ray axis at the frequency W = 2v, the vector end describing a corkscrew-like trajectory. It is easily established that for an observer looking at an incoming light ray, the E-field appears to rotate in the clockwise (cw) direction. In the case 84 = -/2, we obtain a similar conclusion, except that the E-field rotates in the counterclockwise (ccw) direction. In both cases, light is said, therefore, to be circularly polarized. Conventiona