tensor product Hilbert space
When two different quantum systems are considered together, the Hilbert space of the combined system is the tensor product of the Hilbert spaces of the two components. For example, let A and B be two quantum systems, with Hilbert spaces 






H



A




{\displaystyle {\mathcal {H}}_{A}}

 and 






H



B




{\displaystyle {\mathcal {H}}_{B}}

, respectively. The Hilbert space of the composite system is then
