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## Homework Statement

Write the density operator

$$\rho=\frac{1}{3}|u><u|+\frac{2}{3}|v><v|+\frac{\sqrt{2}}{3}(|u><v|+|v><u|, \quad where <u|v>=0$$

In matrix form

## Homework Equations

$$\rho=\sum_i p_i |\psi><\psi|$$

## The Attempt at a Solution

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The two first factors ##\frac{1}{3}|u><u|## and ##\frac{2}{3}|v><v|## pertain to the diagonal elements of the 2x2 matrix, I am unsure how to find the off diagonal elements for this matrix and the ##|u><v|## and ##|v><u|## I don't think are included in the sum I listed in the relevant equations.

In matrix form I have

$$\rho=

\left( \begin{array}{cc}

1 & ? \\

? & 2 \end{array} \right)$$

I have the suspicion that $$\frac{\sqrt{2}}{3}$$ is the offdiagonal elements, however, I don't want to put this down just off of my suspicion. Any tips, or things to think of for me would be appreciated.