# Is there a name for the terms that make up a state?

Suppose I have the state $$\frac{1}{2}(|0\rangle + |1\rangle)$$, how can I refer to ket 0 and ket 1 in general within a state? Would "term 1" and "term 2" work?

## 2 Answers

If you have $$|\psi \rangle = \alpha |0\rangle + \beta|1\rangle$$ then you can refer to $$|0\rangle$$ and $$|1\rangle$$ as the basis states. This is generalize to $$n$$ qubit system as well.

And yes, you can just just refer to them as the $$|0\rangle$$ or "ket 0" state, and $$|1\rangle$$ or "ket 1" state.

Generally, a quantum state $$|\psi\rangle$$ is composed of basis states $$|0\rangle$$ and $$|1\rangle$$. This come from linear algebra where any vector can be written as a sum of basis states multplied by an appropriate number. Since quantum states can be described by vectors from $$\mathbb{C}^{2^n}$$ (where $$n$$ is a number of qubits in the state), term basis states is more than appropriate.

You can also call these states ZERO and ONE in this particular case (a basis composed of $$|0\rangle$$ and $$|1\rangle$$ is called computational basis).

Just note that your state is not normalized, it should be $$\frac{1}{\sqrt{2}}(|0\rangle +|1\rangle)$$. Maybe, you were confused by notion that $$|\psi\rangle$$ collapses to either 0 or 1 with 50 % probability after measurement. However, coefficients in a quantum state are complex numbers called (quantum) amplitudes. A probability is square of amplitude absolute value.