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## Hot answers tagged textbook-and-exercises

6 votes

In fact, we have a more general equality: $${\text Tr}(AB) = {\text Tr}((A\otimes B) S),$$ for any square matrices $A,B$. If $A = |a\rangle\langle b|$ and $B = |c\rangle\langle d|$ then $${\text Tr}... • 7,612 4 votes Accepted ### What is the operator-sum representation of the two-qubit depolarizing channel? As pointed out in the comments, you cannot use the one-qubit formula because something like X\rho X does not make sense if \rho is a 2-qubit state. In fact, for this reason the answer you based ... • 2,823 2 votes ### Prove {\rm tr}(\rho^2)={\rm tr}((\rho \otimes \rho')S) with S the swap operator You can easily prove that identity using graphical notation that depicts tensor contractions by lines: EDIT: It seems like the graphical notation is less known than I anticipated. Doesn't matter. The ... 1 vote Accepted ### Writing a Density matrix in terms of the magnitude of the Bloch Vector Not only is the missing \frac12 is a typo, but the squares are a typo, as well. The easiest way to see this (and to verify OP's solution) is to use the eigenvalue formula for 2\times 2 matrices:$$...
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