# I Phase of |0> when it appears in a product

1. Apr 20, 2017

### Swamp Thing

In a beam splitter with one vacuum input, the output looks like $\frac{1}{\sqrt 2}(|1_A\rangle +i|0_B \rangle)\frac{1}{\sqrt 2}(-i|1_A\rangle +|0_B \rangle)$.
If there is some further processing, the vacuum $i|0_B\rangle$, along with the i , could end up multiplied with some non-vacuum term.

Do we need to keep track of that "i" that originates from such a vacuum term? If so, what is the physical interpretation?

2. Apr 20, 2017

### kith

The state you have given doesn't make sense to me. Are you really familiar with what a products of ket vectors signifies?

3. Apr 20, 2017

### Swamp Thing

4. Apr 20, 2017

### Swamp Thing

Actually, they do keep track of the vac term in that reference so I guess that answers my question.