The Zeno effect can still occur if there's no measurements. Let there be a qubit B and a register of N qubits C[0], C[1], ..., C[N-1]. Now repeat the following

The Zeno effect can still occur if there's no measurements. Let there be a qubit B and a register of N qubits C[0], C[1], ..., C[N-1]. Now repeat the following N times: rotate B by an N'th of a full turn and then perform C[k] ^= B (a CNOT controlled by B targeting C[k] where k is the index of the iteration). These are all unitary operations; no measurement. If you consider doing this for larger and larger N, you find that if B started in the |0> state then B ends up nearer and nearer the |0> state as N increases. B's final density matrix limits to |0><0| as N goes to infinity.