7.3 The complex math and physics of a single qubit

Let’s revisit our definition of a qubit from section 7.1. This time, we break it into two pieces: a mathematical and a physical/quantum mechanical part.

Mathematics

A qubit—a quantum bit—is the fundamental unit of quantum information. At any given time, it is in a superposition state represented by a linear combination of vectors |0⟩ and |1⟩ in C²:

Physics

Through measurement, a qubit is forced to collapse irreversibly to either |0⟩ or |1⟩. The probability of its doing either is |a|² and |b|², respectively. a and b are called probability amplitudes.

When we measure, do we get a bit 0 or 1, or a qubit |0⟩ or |1⟩? Technically, it is the former, but by abuse of notation, we often show it as the latter. You can only get 0 when you measure |0⟩, and you can only get 1 when...