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 $\ket{\Psi^+} = \frac{1}{\sqrt 2}(\ket{00} + \ket{11})$.
page revision: 0, last edited: 18 Nov 2012 18:15
a. $\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}$
b. $\frac{1}{\sqrt2} \begin{pmatrix} 1 & -i \\ 1 & i \end{pmatrix}$
c. $\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}$
d. $\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \end{pmatrix}$
e. $\frac{1}{2}\begin{pmatrix} 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 \end{pmatrix}$