Exercise 3.7 Discussion

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 3.7}$

Write the following states in terms of the Bell basis.

a) $\ket{00}$

b) $\ket{+}\ket{-}$

c) $\frac{1}{\sqrt 3}(\ket{00} + \ket{01} + \ket{10})$

page revision: 1, last edited: 11 Dec 2011 23:16

Using the notation for Bell states given in the text:

a.$\ket{00} = \frac{1}{\sqrt{2}} \big( \ket{\Phi^{+}} + \ket{\Phi^{-}} \big)$,b.$\ket{+}\ket{-} = \frac{1}{2}\big( \ket{00} - \ket{01} + \ket{10} - \ket{11}\big) = \frac{1}{\sqrt{2}}\big( \ket{\Phi^{-}} - \ket{\Psi^{-}}\big)$, andc.$\frac{1}{\sqrt{3}}\big( \ket{00} + \ket{01} + \ket{10}\big) = \frac{1}{\sqrt{6}}\ket{\Phi^{+}} + \frac{1}{\sqrt{6}}\ket{\Phi^{-}} + \sqrt{\frac{2}{3}} \ket{\Psi^{+}}$.ReplyOptionsIMHO, a better presentation of c) would be

$\frac{1}{\sqrt{6}} (\ket{\Phi^+} + \ket{\Phi^-} + 2\ket{\Psi^+} )$

which reveals a nice structure. (Sorry for nitpicking).

ReplyOptions