nce that one atom decays, which is recorded by the Geiger counter. In this event, the counter activates the opening of the poison-gas can, resulting in the cat's instant death. At any time, the (poor) cat's state can be viewed as a superposition of the pure states |dead) or |alive), Quantum bits and quantum gates of the sleeping toddler, and of Schrödinger's cat illustrate the same paradox: does the state of a macroscopic object or system require an outside observer to be defined, or is it self-defined independent of outside observation? Our intuition tells us that such an object or system cannot exist in two states at the same time, and, therefore, it must be its own "observer." The quantum-mechanics viewpoint breaks with intuition and affirms the contrary: that objects or systems can, indeed, exist in multiple states, and that only the observer intervention defines what the actual state turns out to be. About elementary information, our classical mind training requires that a bit is absolutely defined as either being 0 or 1 (regardless of possible measurement mistakes). With the qubit, we must now retrain our mind to accept the fact that a quantum of information (the qubit) is in a 0/1 superposition state, whose outcome in observed reality remains undefined until some measurement is performed. The next two chapters will clarify and further develop such a most intriguing notion! To summarize the above description SO far, a qubit must be conceived as a two- dimensional bit, whose coordinates in that space represent probability amplitudes. Since two coordinates define the qubit, it is possible to represent it as a unique point on the sur- face of a sphere of unity radius, called a Bloch sphere, which is described in Appendix M. In this appendix, it is shown that the most general definition of the qubit, within an unob- servable phase factor, is (16.7) The two angles A, Q, thus, uniquely define the position of a point on the surface of a sphere, just like latitude and longitude on the Earth, and as illustrated in F