I'm currently reading this paper https://arxiv.org/abs/quant-ph/0403062 but I fail to understand how the input of the control qubit affects the output of the target qubit. I do understand that when the logical value of the control qubit channel is $\vert 0\rangle$ the qubit in the channel of the target qubit is not affected. But I don't see how does the gate work when the control and target qubit have a logical value of $\vert 1\rangle$.
In (O'Brien et al. 2004), why is the target qubit not affected when the control is $\vert 0\rangle$?
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4$\begingroup$ quoting or including in the post the relevant parts of the paper would make the question easier to answer without people having to go read the paper itself $\endgroup$– glS ♦May 27, 2021 at 19:16
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$\begingroup$ Looks like they cited this paper regarding the CNOT they implement: arxiv.org/pdf/quant-ph/0112088.pdf $\endgroup$– chrysaor4May 28, 2021 at 9:57
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