t the source tone is A or B, respectively. The other two successful measurements (A, 3) (B, 3), like all failed measurements, do not convey any information, as mentioned earlier. The success of our measurement and the absolute conclusion therein, is, thus, dependent on our filter choice (1 or 2), which is essentially a matter of guesswork. From any academic standpoint, it remains debatable whether the above fictitious "physical measurement" through a set of "magic filters" may, in some way, help clarify the essence of a true quantum POVM measurement. If it has any merit, however, it helps to stress the point that quantum measurements are based on the observer's choice of a measurement operator (the magic filter). The measurement or observation of an outcome may either succeed or fail (seeing or not seeing a spot). In the case of success, 17.3 Quantum measurements on joint states Figure 17.1 Fictitious analogy of POVM measurement of tones A, B and a magic-filter set 1, 2, 3 to characterize a source. Given the tones A, B and choices 1, 2, 3, a positive observation of the tone is characterized by the bright spot on the images shown, with various probabilities 0, 1, p, 1 - p. The two images marked with a cross (x) correspond to absolutely certain measurements that the source tone is A or B. the observer may or may not be able to derive an absolute conclusion as to what state was observed (the source tone), depending on his or her choice. Leaving fiction behind, we can conclude that POVM measurements make it pos- sible to get absolutely certain information about the input state 1/s/, despite the fact that it is, a priori, unknown, just as the right measurement operators are unknown. We have noted that while the corresponding measurements may sometimes fail, the conclusion is never wrong when they succeed. This remarkable property is referred to as unambiguous quantum state discrimination, of UQSD. Remarkably, while UQSD has no classical explanation, or no counterpart in classical physics, it can be imple- mented in ac