I am a bit confused by the following scenario:
Suppose we are given an entangled state $| \psi \rangle$ that has $2$ qubits (we can generalize to $n$ qubits).
Suppose we had a circuit like above. Because $| \psi \rangle$ is entangled, we cannot really CNOT each qubit, or Hadamard a single qubit. So how would we predict an outcome of such a circuit in general, mathematically?
And how could we extend this to more complex gates, like a CSWAP?