I'm trying to understand how the Deutsch–Jozsa algorithm works with the following circuit:
Since we have the top 2 wires measuring $|0\rangle$ with 100% probability, it means $U_f$ is constant. And that's what I'm having trouble understanding...what exactly is constant?
If I isolate $U_f$ I get this: Oracle function
I understand the concept of balanced and constant functions, and that an n-bit binary string will have $2^n$ mappings, which gives $2^n$ possible functions. So how can I see that $f$ is constant in the isolated circuit above?