Undergrad Question about No-Cloning Theorem and State Tomography

[Irishdoug]

TL;DR

Question about No-Cloning Theorem and State Tomography

Hi,

I have a question, or am looking for clarification, about the no-cloning theorem and state tomography. My understanding is that the theorem states one cannot make an exact copy of a quantum state. I was also reading about state state tomography where it was said*

'On the other hand, the no-cloning theorem forbids one to create a perfect copy of the system without already knowing its state in advance. Thus, there is no way out, not even in principle, to infer the quantum state of a single system without having some prior knowledge on it [4]. It is possible to estimate the unknown quantum state of a system when many identical copies are available in the same state, so that a different measurement can be performed on each copy. A procedure of such kind is called quantum tomography.'

How can it be, if one cannot create a perfect copy of a state, one can create many identical copies that are in the same state?

Is it the case that you can (attempt to) prepare each state in the same way, but that each state will be slightly different from last?

*ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL. 128 Quantum Tomography G. MAURO D'ARIANO, MATTEO G. A. PARIS, and MASSIMILIANO F. SACCHI

 

[martinbn]

How can it be, if one cannot create a perfect copy of a state, one can create many identical copies that are in the same state?

It means that if you have a quantum mechanical system, and you don't know anything about it, you cannot use it to make identical copies of it. But if you know how it was prepared in the first place, you can simply prepare many systems in the same way. You are not using the given system, you are using the same method of preparation.

 

[f95toli]

Note also that tomography is in practice very often used to test just how well you are able to control/prepare your system.
That is, the assumption is then that the results of of subsequent measurements would end up being nominally identical if you were able to prepare your system with 100% fidelity.

 

[Irishdoug]

Thanks to both of you.

 

[George Jones]

The no-cloning theorem theorem says that an identical copy cannot be made while retaining the original. An identical copy of an arbitary quantum state can be made if the original state is destroyed, e.g., quantum teleportation (also involves passage of some classical information).