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What is a 'bipartite unitary'? I saw it appearing in a paper "Efficient verification of quantum gates with local operations" (https://arxiv.org/pdf/1910.14032.pdf)

A reference to the definition is very much appreciated.

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    $\begingroup$ A unitary acting on a bipartite system? $\endgroup$
    – Rammus
    Jul 7, 2021 at 20:49
  • $\begingroup$ I am curious, is your user name based off the league of legends character? and yes I would think that makes sense. I am trying to find a reference to the definition. $\endgroup$ Jul 7, 2021 at 21:13
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    $\begingroup$ related: quantumcomputing.stackexchange.com/q/6052/55 $\endgroup$
    – glS
    Jul 7, 2021 at 21:21
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    $\begingroup$ @QuantumGuy123 You got me $\endgroup$
    – Rammus
    Jul 7, 2021 at 21:44

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Take operators $A_n$ and $B_n$ that act on systems $a$ and $b$ respectively. A bipartite unitary can be written as $$ U=\exp(i \sum_n A_n\otimes B_n), $$ any time that the construction $\sum_n A_n\otimes B_n$ is Hermitian.

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  • $\begingroup$ how does the exp of a matrix equal a matrix? $\endgroup$ Jul 7, 2021 at 21:16
  • $\begingroup$ do you have a reference anywhere for this definition? $\endgroup$ Jul 7, 2021 at 21:16
  • $\begingroup$ also, does Rammus' comment suffice as an answer? "A unitary acting on a bipartite system" $\endgroup$ Jul 7, 2021 at 21:17
  • $\begingroup$ Yes, Rammus's comment is correct. Then, unitary operators $U$ can always be constructed as exponentials of Hermitian operators $H$ via $U=\exp(i H)$, so any bipartite Hermitian operator $H$ can be used to create a bipartite unitary operator $U$. $\endgroup$ Jul 7, 2021 at 21:32
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    $\begingroup$ en.wikipedia.org/wiki/Matrix_exponential $\endgroup$ Jul 7, 2021 at 21:33

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