Solution to Exercise 3.7.

FlippingBits 31 May 2014 00:30

Using the notation for Bell states given in the text:

**a.** $\ket{00} = \frac{1}{\sqrt{2}} \big( \ket{\Phi^{+}} + \ket{\Phi^{-}} \big)$,

**b.** $\ket{+}\ket{-} = \frac{1}{2}\big( \ket{00} - \ket{01} + \ket{10} - \ket{11}\big) = \frac{1}{\sqrt{2}}\big( \ket{\Phi^{-}} - \ket{\Psi^{-}}\big)$, and

**c.** $\frac{1}{\sqrt{3}}\big( \ket{00} + \ket{01} + \ket{10}\big) = \frac{1}{\sqrt{6}}\ket{\Phi^{+}} + \frac{1}{\sqrt{6}}\ket{\Phi^{-}} + \sqrt{\frac{2}{3}} \ket{\Psi^{+}}$.