Pure Quantum State

quantum-computing

Definition

Pure Quantum State

Let $\mathcal{H}$ be a complex Hilbert space. A pure quantum state is a quantum state represented by a single ray in $\mathcal{H}$: an equivalence class

$$[|\psi ⟩]=\{e^{i\theta }|\psi ⟩\mid \theta \in \mathbb{R}\}$$

where $|\psi ⟩\in \mathcal{H}$ is normalised, i.e. $⟨\psi |\psi ⟩=1$.

A quantum state that is not pure is a mixed quantum state.