No Cloning Theorem: Understand Why It Violates Uncertainty

[desmal]

Hi everyone,


I have couple questions about the no cloning theorem. It states that a quantum state can't be precisely copied.

1-Can you explain to me in very simple words why this theorem violat the uncertainty principle?

2-Also when I read the prove of the theorem, I couldn't understand some of the bra-ket manipultations used to prove this theorem like, when a state is copied we can represent that like:-
G--> |G> |G> two ket product!
bra and ket can be maltiplied since in matrices one is a coulumn and the other is a row and moreover I know how to represent them as an integeral. But ket with ket product make no sense for me both as an integral or in matrix representation.

 

[DrClaude]

1-Can you explain to me in very simple words why this theorem violat the uncertainty principle?

Good question. I don't see why it would violate the uncertainty principle, since nothing forbids you to simply prepare a series of quantum systems in the same state, on which you could perform any series of measurements.

See also the discussion here:
https://www.physicsforums.com/threads/no-cloning-and-uncertainty-principle.748469/

2-Also when I read the prove of the theorem, I couldn't understand some of the bra-ket manipultations used to prove this theorem like, when a state is copied we can represent that like:-
G--> |G> |G> two ket product!
bra and ket can be maltiplied since in matrices one is a coulumn and the other is a row and moreover I know how to represent them as an integeral. But ket with ket product make no sense for me both as an integral or in matrix representation.

It is the direct product $|G\rangle \otimes |G\rangle$, where each ket corresponds to a different particle.
https://theory.physics.manchester.ac.uk/~judith/AQMI/PHYS30201su9.xhtml