Exercise 3.14 Discussion

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 3.14}$

a) For the standard basis, the Hadamard basis, and the basis $B = \{\frac{1}{\sqrt 2}(\ket 0 + \i\ket 1, \ket 0 - \i\ket 1 \}$, determine the probability of each outcome when the second qubit of a two-qubit system in the state $\ket{00}$ is measured in each of the bases.
b) Determine the probability of each outcome when the second qubit of the state $\ket{00}$ is first measured in the Hadamard basis and then in the
basis $B$ of part a).
c) Determine the probability of each outcome when the second qubit of the state $\ket{00}$ is first measured in the Hadamard basis and then in the standard basis.