Summary: Qubits and Quantum States

Here are the key takeaways:

• Qubits are actual physical objects whose properties we can measure. For qubits, there are two possible results for the measurement outcomes.

• The associated quantum states are represented by state vectors in an abstract two-dimensional state space analogous to a classical vector in physical space with $x$ and $y$ spatial coordinates. A state vector can be represented by right vector symbols $\vert A\rangle$, by arrows in a state space diagram, and by column vectors.