Editing Projective Hilbert space (section)

==Product==
The [[Cartesian product]] of projective Hilbert spaces is not a projective space. The [[Segre mapping]] is an embedding of the Cartesian product of two projective spaces into the projective space associated to the [[tensor product]] of the two Hilbert spaces, given by <math>\mathbf{P}(H) \times \mathbf{P}(H') \to \mathbf{P}(H \otimes H'), ([x], [y]) \mapsto [x \otimes y]</math>. In quantum theory, it describes how to make states of the composite system from states of its constituents. It is only an [[embedding]], not a surjection; most of the tensor product space does not lie in its [[range of a function|image]] and represents ''[[quantum entanglement|entangled states]]''.