Summary: Putting a Spin on Spin

Here are the key takeaways:

• Spin states are a paradigmatic example of qubits, with the two basis states being spin-up and spin-down. They offer a testbed to practice and review the fundamentals we have covered so far.

• Spin-½ states are an example of the difference between physical states and quantum space states. A particle flipping from a spin-up to a spin-down has, in a sense, changed its physical spin orientation by $180\degree$ (but see the caveat about spin-up and spin-down at the end of the Quantum Gates and Spin-1/2 Systems lesson). In the quantum state space, however, the change is only $90\degree$ because the abstract state-space basis vectors are orthogonal.