# Generalized Teleportation Protocol simple case with 1 qubit problems with calculations

Hello to everyone,

I am an undergraduate student and for a course I need to read and to undersand this article. And I have some difficulties to understand some parts of it.

I would be happy if somebody was able to explain me in details each step on how did they get those results (mostly (7) and (8) ):

Or at least if you can detail me the calculus of only one of the result above it will be allready great.

For example concerning the first result: $$\langle P_{\phi^+_m}\rangle = \frac{1+|nm|^2}{2(1+|n|^2)(1+|m|^2)}$$
My computation reads as follows: \begin{align*} \langle P_{\phi^+_m}\rangle = \langle \psi| \phi^+_m\rangle \langle \phi^+_m |\psi \rangle = \ldots&= NL (\alpha^* \langle 0|_B + \beta^* n^* l \langle 1|_B) NL (\alpha |0\rangle _B + \beta n l^* |1\rangle _B) \\&= \frac{1}{(1+|n|^2)(1+|l|^2)} (1+|nl|^2) \end{align*} and I do not get the $$2$$ in the denominator.

Reminder: $$| \psi \rangle$$ is equal to

Thank a lot for your help.

• up, anyone to help me? Commented Aug 2 at 19:23