No Cloning Theorem: Understand Why It Violates Uncertainty

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In summary, the no cloning theorem states that a quantum state cannot be precisely copied. This raises questions about how it relates to the uncertainty principle. The proof of the theorem involves bra-ket manipulations, such as representing copied states as a direct product of two kets. However, this concept can be difficult to understand, especially in terms of integrals or matrix representations.
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desmal
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Hi everyone,


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

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

2-Also when I read the prove of the theorm, I couldn't understand some of the bra-ket manipultations used to prove this theorm 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.
 
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desmal said:
1-Can you explain to me in very simple words why this theorm 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/
desmal said:
2-Also when I read the prove of the theorm, I couldn't understand some of the bra-ket manipultations used to prove this theorm 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
 

1. What is the No Cloning Theorem?

The No Cloning Theorem states that it is impossible to create an identical copy of an unknown quantum state. This means that it is not possible to clone a quantum system without having complete knowledge of its state, which violates the principle of uncertainty in quantum mechanics.

2. How does the No Cloning Theorem violate uncertainty?

The No Cloning Theorem violates uncertainty because it assumes that it is possible to have complete knowledge of a quantum state, which goes against the principle of uncertainty in quantum mechanics. This principle states that it is impossible to simultaneously know the exact position and momentum of a quantum particle, and the No Cloning Theorem relies on having this information in order to clone a quantum system.

3. Why is the No Cloning Theorem important in quantum computing?

The No Cloning Theorem is important in quantum computing because it sets a limit on the amount of information that can be copied or shared between quantum systems. This means that quantum computers cannot rely on copying and pasting information like classical computers do, and instead must use other methods such as entanglement to transfer information between qubits.

4. Are there any exceptions to the No Cloning Theorem?

No, there are no known exceptions to the No Cloning Theorem. It is a fundamental principle in quantum mechanics and has been proven mathematically.

5. How does the No Cloning Theorem impact quantum cryptography?

The No Cloning Theorem has a significant impact on quantum cryptography because it ensures the security of quantum communication. Since it is impossible to clone a quantum state, any attempt to intercept and copy information in a quantum communication system will result in a loss of information, making it possible for the intended recipient to detect tampering. This makes quantum cryptography a much more secure method of communication compared to classical cryptography.

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