# Arbitrary two qubit unitaries using SWAP gate instead of CNOT gate

An arbitrary two qubit gate can be constructed using local operations with CNOT gate. Are there other ways to implement these gates in this manner? In particular, can I decompose a two qubit gate in terms of local operations and SWAP gate? (The problem is solved if we can just write CNOT gate in terms of SWAP and local operations).

(What makes a gate one that creates entanglement? Assume it is a unitary $$U$$. If there exists a product state $$|\psi\rangle|\phi\rangle$$ such that $$U|\psi\rangle|\phi\rangle$$ is not a product state, then $$U$$ is entangling.)