I have two gates here for the Grover diffusion operator. The first gate is completely understandable for me, so I implemented it myself after submitting some papers that I read. This is the first gate (understandable for me):

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Recently, however, I have seen an implementation of the Grover algorithm in which the diffusion operator still uses the oracle qubit. My question is, what does this circuit do? And why does it work?

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