Exercise 2.13

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 2.13}$

Relate the four parametrizations of the state space of a single qubit to each other: Give formulas for

a) vectors in ket notation

b) elements of the extended complex plane

c) spherical coordinates for the Bloch sphere (see exercise 2.12) in terms of the $x$, $y$, and $z$ coordinates of the Bloch sphere.

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