Entangled Quantum State

quantum-computing

Definition

Entangled Quantum State

Let ${\mathcal{H}}_{AB}$ be the composite state space of two quantum systems $A$ and $B$. A pure quantum state $|\psi ⟩\in {\mathcal{H}}_{AB}$ is entangled across the cut $A\mid B$ iff it cannot be written as a product state:

$$|\psi ⟩\ne |a⟩\otimes |b⟩$$

for any normalised $|a⟩\in {\mathcal{H}}_A$, $|b⟩\in {\mathcal{H}}_B$.

A state that is not entangled is a separable quantum state.