The cnot with outer product control qubit

[Galaxion]

I have a simple question...the control qubit is A and the the target is B.
The cnot is applied on |1_A> <0_A|⊗|0_B0_C>.
...
How does it work.
Thanks in advance.

 

[jedishrfu]

First here's wikipedia's discussion on it:

https://en.wikipedia.org/wiki/Controlled_NOT_gate

and further on medium:



and here's how a QC works: