Composite State Space (Quantum Computing)

quantum-computing

Definition

Composite State Space (Quantum Computing)

Let $A$ and $B$ be quantum systems with state spaces ${\mathcal{H}}_A$ and ${\mathcal{H}}_B$. Their composite state space is the tensor product

$${\mathcal{H}}_{AB}={\mathcal{H}}_A\otimes {\mathcal{H}}_B.$$

For $n$ subsystems, the composite state space generalises to

$$\mathcal{H}={\mathcal{H}}_1\otimes {\mathcal{H}}_2\otimes \cdots \otimes {\mathcal{H}}_n.$$

A state in the composite space that is not a tensor product state is entangled.