The shell command<br />"/lrn-mdl-prod/build/71719/filter/tex/mimetex.linux" -e "/lrn-mdl-prod/moodledata/filter/tex/8849338bdb4989dadbda1bc6d1786d89.gif" -- '\Large  \begin{split} \rho_A                 &= \text{tr}_B(\rho_{AB}) \\                 &= \frac{1}{2}\left\{\text{tr}_B(|0_A0_B\rangle\langle0_A0_B|) + \text{tr}_B(|0_A0_B\rangle\langle1_A1_B|) + \text{tr}_B(|1_A1_B\rangle\langle0_A0_B|) + \text{tr}_B(|1_A1_B\rangle\langle1_A1_B|)\right\} \\                 &= \frac{1}{2}\left\{\text{tr}_B(|0_A\rangle\langle0_A|\otimes|0_B\rangle\langle0_B|) + \cdots \right\} \\                 &= \frac{1}{2}\left\{|0_A\rangle\langle0_A|\langle0_B|0_B\rangle + |0_A\rangle\langle1_A|\langle1_B|0_B\rangle + |1_A\rangle\langle0_A|\langle0_B|1_B\rangle + |1_A\rangle\langle1_A|\langle1_B|1_B\rangle\right\} \\                 &= \frac{1}{2}\left\{|0_A\rangle\langle0_A| + |1_A\rangle\langle1_A|\right\} = \frac{1}{2}\mathbf{I}.                 \end{split} '<br />returned status = 1<br />
Image not found!<br />Please try the <a href="https://lo.unisa.edu.au/filter/tex/texdebug.php">debugging script</a>