Product state

Each wire has its own amplitudes, and each joint number is a product of one amplitude from each wire. The 01 and 11 bars are empty because the second wire is the state certain to read 0.

A product state is a joint state that splits into one line of amplitudes for each wire. Each of the four joint numbers, on 00, 01, 10 and 11, is the product of one amplitude from the first wire and one from the second.

The two-wire note starts from a product, the |+⟩ state on the first wire and the state certain to read 0 on the second, which puts amplitude on 00 and on 10 only. The controlled NOT rewrites the 10 term as 11, and the state that remains will not split back into a line per wire.

Product state

Used in