tive, or successful, measurement (seeing something). The absence of spot indicates a negative, or failed, measurement (not seeing anything). Considering first the case of pure tones (A or B), the figure indicates that there are actually two "successful" measurement outcomes, as characterized by the presence of the bright spot with nonzero probability. These successes correspond to the two input or filter cases (A, 0), (B, 1), which positively identify the tones to be A or B with absolute certainty (p = 1 for A, or g = 1 - p = 1 for B). In the two other cases, (A, 1), (B, 0), we never see any spot, or the measurement is always "failed." But here comes a subtlety: if we know prior to the measurement that the color tones are pure, the failed measurement is also a positive indication. Indeed, a failure to measure A means an absolute certainty that the input is B, and the reverse. The certainty is the same regardless of our filter choice (0 or 1). In this case, the classical bit measurement from the qubit is 100% accurate. The 18.1 Measuring single qubits Figure 18.1 Fictitious analogy of qubit measurement of tones A, B, or their mixture, and a magic-filter set 0, 1 to characterize a source. Given the tones A, B and choices 1, 2, a positive observation of the tone is characterized by the bright spot on the images shown, with various probabilities 1, 0, p, 1 - p. information gained is a 0 or 1 classical bit, in 100% correspondence with the qubit pure state. But to achieve this performance without any concern for the measurement option (Mo, M1), it costs the tax of one bit of advance information (i.e., "pure input state?" = YES, NO). In the case of the tone mixture (Fig. 18.1, right) we observe only two measurement "successes," with probability p when using the filter 0, and probability 1 - p when using the filter 1. The information obtained in these two cases is a classical bit of information 0 or 1, as we have projected the qubit onto the corresponding pure states. But, as the figure indicates, there is a finite proba