I am a curious quantum computing learner. :)

Once observe the CNOT gate: enter image description here

as you can see there it converts a |+> to |-> in the top or to say in another way it clones the |->

state. So does this violate "No Cloning Theorem".

Say for example when you apply a CNOT gate to a qubit in superposition then that is indeed as the

same as cloning the qubit in superposition.


1 Answer 1


Cloning means you have a unitary transforming $U$ that takes $|\psi\rangle|0\rangle $ to the $|\psi\rangle|\psi \rangle $ for all quantum states $|\psi\rangle$. That is,

$$ U\big(|\psi\rangle|0\rangle \big) = |\psi\rangle|\psi \rangle \hspace{0.5 cm} \forall \ |\psi \rangle \in \mathcal{H} $$

where $\mathcal{H}$ is a Hilbert space. Thus, what you shown is not a violation of the no cloning theorem.

Note that the no-cloning theorem tells us that it is impossible to clone a specific unknown quantum state, but it does not preclude the construction of a known quantum state from a known quantum state.


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