does there exist a quantum approximate cloning method that does not modify the initial qubit (the one whose state we want to clone)?

Question

I am currently trying to implement circuit (in Qiskit if that is relevant) to approximate a state of a qubit without measuring it (basically I want to "attach it" to a qubit and have some approximate idea about it's state while not collapsing it's quantum state and not changing it)

I have looked at Universal Quantum Cloning Machine:

I have noticed that this does seem to change the state of the input qubit (I had an input state of |1> but some of the post measurements returned 0 in a simulator).

is anyone aware of an approach that allows to approximate state of a qubit without changing it? (is that even possible under no cloning theorem or any other restrictions coming from quantum mechanics?)

I would be very grateful for any pointers

Answer 1

It's not possible to make an approximate clone of a qubit without ever affecting that qubit. Otherwise you could just keep approximate-cloning, do tomography on the clones to confidently learn the direction of their Bloch vector (which will point in the same direction as the original qubit), and extend that vector to the surface of the Bloch sphere infer the state of the original qubit.

All information extraction procedures have kickback onto the target qubit. You cannot get around this.