A quantum state can be represented as linear combination of 2 states:
In Chuang and Nielsens book, it states that because the squared amplitudes sum to 1:
That the combination can be rewritten as:
My first question is, why exactly is this? And secondly, how is this state represented in the bloch sphere?
I am aware that this may be a simple question to many, but a step by step walkthrough of the algebra underlaying the bloch representation of the qubit would be immensely helpful to me and some friends.