I am a bit confused about the necessity of an oracle qubit in Grover's algorithm.
My question is, does it depend on how you implement your oracle whether you need an oracle qubit or not? Or, it there any reason for an oracle qubit? (such as, there exist some problems that cannot be solved without an oracle qubit, or it's easier to think about the problem with an oracle qubit, or it's a convention, etc)
Many resources introduce Grover's algorithm with an oracle qubit, but I found there are some cases that you do not need an oracle qubit.
For example, here are two implementations of Grover's algorithm in IBM Q simulator. One is using an oracle qubit, and the other is not. In both cases, I would like to find |11> from a space of |00>, |01>, |10>, and |11>. In both cases, oracle successfully flips |11> to -|11>.
・With an oracle qubit (Link to IBM Q simulator)
・Without an oracle qubit (Link to IBM Q simulator)