By S S Schweber

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6. Obviously, 1v = v for any amplitude vector v. We can represent each of these graphically using a modiﬁcation of our previous diagrams. From now on we will draw the upper and lower beam paths as parallel lines, except where they are brought together at a beamsplitter or a beam crossing. The photon is assumed to go from left to right, see Fig. 4 What happens when the basic optical elements are assembled into a larger experiment? In a diagram, we simply string the pieces together in sequence, as in Fig.

Worse, once we have measured Sx , 9 This is quite similar to a simple lecture demonstration involving polarizing ﬁlters. Polarization is a property of photons that is exactly analogous to particle spin. A polarizing ﬁlter blocks light of one polarization, but permits light of the other (perpendicular) polarization to pass. No light can get through a pair of “crossed” polarizing ﬁlters. But if a third tilted ﬁlter is introduced between the pair, some of the photons do pass through. 36 Qubits the particle will have “forgotten” all about its previous state.

This is illustrated in Fig. 14. Later in this book we will discuss at length how the complicated structure of energy levels emerges from the quantum physics of the interacting nucleus and electrons in an atom. For now, we will simply take that structure as a given and begin to explore what it entails. A particular type of atom generally has many different energy levels. In many experiments, though, only two energy levels – usually the ground state and one excited state – play any signiﬁcant role.

### An introduction to relativistic quantum field theory by S S Schweber

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