Yes you need to worry about charlie’s part too. There will be no cross term in the expansion of the square norm equ (12) because the states 0 and 1 of charlie are orthogonal! Then you find (13) with no double product cross term! Which eventually leads to 1/2 in (14).
In your handwritten calculation i dont ser the bits of Charlie, hence this calculation is probably wrong.
In your handwritten calculation i dont ser the bits of Charlie, hence this calculation is probably wrong.
