 |->. Thus, the positive outcome of any E3 measurement only tells us that the system state is neither |1) or |-), but we already know this for a fact, which represents no information! Therefore, there is no point in using E3 as a means to measure the system state. Let me, then, clarify what is meant by "positive outcome" and "failure" of any of the above measurements, using a figurative analogy with a physical measurement. Compare the system state /v/s to a light source that randomly emits in two possible color tones, either A or B (standing for |0) or |+), respectively), these tones being invisible to the naked eye. Our measurement consists of determining which color tone is emitted by the source by observing it through a set of "magic filters," called 1, 2, 3, (for E1, E2, E3). Such filters have the following strange properties: filter 1 does not react to tone A, while it makes tone B visible to the eye with probability p (or u/2); filter 2 does not react to tone B, while it makes tone A visible to the eye with same probability p; and filter 3 does not react to any tone other than A, B (but this is not useful here) but makes tone A, B visible with probability 1 - p (or 1 - u/2). Basically, if we choose either filter 1 or filter 2, we have a chance p of seeing something, and 1 - p of seeing nothing! Figure 17.1 shows what we can see through the magic filters, according to the twelve possible cases, namely, determined by the two source-tone possibilities A, B and our three possible magic-filter choices 1, 2, 3. A bright spot indicates that we observe some- thing, corresponding to a "positive" measurement. The absence of a spot, or dark image indicates a "negative" or "failed" measurement. The figure shows that the combina- tions (A, 1) and (B, are certain to fail, while the other combinations (A, 2) (B, 1) or (A, 3) (B, 3) have a finite chance, p or 1 - p, respectively, of succeeding. The suc- cessful measurements in the two cases (A,2 2) or (B, 1), as marked with a cross (x), correspond to absolute certainty tha