# What is a bipartite unitary?

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.

• A unitary acting on a bipartite system? Jul 7, 2021 at 20:49
• 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. Jul 7, 2021 at 21:13
• – glS
Jul 7, 2021 at 21:21
• @QuantumGuy123 You got me Jul 7, 2021 at 21:44

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.
• 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 $U$. Jul 7, 2021 at 21:32