I have recently been reading about spontaneous parametric down conversion(SPDC). I do clearly understand the process. What has been intriguing lately is the notation. For those of you who are unfamiliar, SPDC is a process which converts one vertically polarized photon to two horizontally polarized photon. (Yeah, it's not 100% accurate, but just to get the idea across.)
Many paper wrote: $ \left|V\right\rangle \rightarrow \left|H\right\rangle\left|H\right\rangle$
I was just wondering about the meaning of $\left|H\right\rangle\left|H\right\rangle$ since it's neither the inner product nor the outer product. Additionally, if $\left|H\right\rangle$ could be represented by the vector $(1,0)$, what could be the implications?