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Applies to questions of primarily educational value - styled in the format similar to that found in textbook exercises. This tag should be applied to questions that are (1) stated in the form of an exercise and (2) at the level of basic quantum information textbooks.
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Decomposition of a $4 \times 4$ unitary matrix
Note the following: if we have a vector with 2 entries $\begin{bmatrix} a \\ b \end{bmatrix}$, then we can use a unitary matrix to change the second entry to $0$. Namely, set $r = \sqrt{|a|^2 + |b|^2} …
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Quantum Cryptography without Bell's Theorem -- Brassard - Bennett - Mermin
Whether the conjugation transposes tensor factors or not, I think, depends on the convention.
The authors chose to write a bra in $(\mathcal{V} \otimes \mathcal{A})^*$ as $\left<a\right| \left<u\right …