In a book for quantum information, I found the following expression:
$$\sum_{x_0\in\{0,1\}^n}4\big\|\langle x_0|\phi^k\rangle|x_0\rangle\big\|^2=1$$
If so, would not it be 4 as a result? Now, I would just like to know how the result comes out to be 1? I already have a guess, but I can not describe it good enough, or put into the right words.
For information: $|\phi^k\rangle$ is defined as follows $|\phi^k\rangle=U_KU_{k-1}...U_2U_1|\phi\rangle$, where $U_K$ means a unitary transformation.
Can somebody explain to me clearly, or at least comprehensibly, why the result of this expression is 1?
I hope the question is understandable. I hope that the title is ok, if not let me know and I will improve! If you need more information, let me know.