I am very new to Quantum Information. I had the following question on two no-go theorems:
The No cloning theorem states there is no unitary operator $U$ such that $U|\psi\rangle|0\rangle=|\psi\rangle|\psi\rangle$ for all state $|\psi\rangle$. The No deletion states there is no unitary operator $U$ such that $U|\psi\rangle|\psi\rangle=|\psi\rangle|0\rangle$ for all state $|\psi\rangle$. Doesn't the last statement follows from the first after taking $U^*$ on both sides. Also the corresponding wikipedia article mentions it is a time-reversed dual to the no-cloning theorem, so is there some categorical implication?