3 Spin and Qubits

The first chapter described measurements involving the spin of an electron. We saw that if you measure the spin in the vertical direction, you don't obtain a continuum of values, but just two of them: Either the electron has its north pole vertically upward, or it is vertically downward. If we measure the spin first in the vertical direction and then once more in the same direction, we obtain exactly the same result for both measurements. If the first measurement shows that the electron has its north pole upward, then so will the second measurement. We also saw that if we measure first in the vertical direction and then in the horizontal direction, the electrons will have spin N and S in direction 90° each with probability of one half. It doesn't matter what the first measurement is; the second measurement will give a random choice of either N or S. The second chapter introduced the mathematics of linear algebra. The goal of this chapter is to combine these previous two chapters, giving a mathematical model that describes the measurement of spin. We will then show how this relates to qubits. But before we start this description, we introduce the mathematics of probability.