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## Main Question or Discussion Point

Suppose [tex]\mathbf{U}_f(\left| x\right>\left| y\right> )=\left| x\right>\left| y\oplus f(x)\right>[/tex] denotes the unitary transformation corresponding to some 1-bit function f.

I'm guessing here that x is the input register, and y the output register.

Now suppose f(0)=0 and f(1)=0.

How is it that [tex]\mathbf{U}_f=\mathbf{1}[/tex] the 2-Qbit unit operator?

I'm guessing here that x is the input register, and y the output register.

Now suppose f(0)=0 and f(1)=0.

How is it that [tex]\mathbf{U}_f=\mathbf{1}[/tex] the 2-Qbit unit operator?

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