Ex4 1

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 4.1}$

Give the matrix, in the standard basis, for the following operators

a) $\ket{0}\bra{0}$.

b) $\ket{+}\bra{0} - \i \ket{-}\bra{1}$.

c) $\ket{00}\bra{00} + \ket{01}\bra{01}$.

d) $\ket{00}\bra{00} + \ket{01}\bra{01} + \ket{11}\bra{a01} + \ket{10}\bra{11}$.

e) $\ket{\Psi^+}\bra{\Psi^+}$ where $\ket{\Psi^+} = \frac{1}{\sqrt 2}(\ket{00} + \ket{11})$.