# Re: Copying?

```2009/2/22 Stephen Paul King <stephe...@charter.net>:

>     Ok, my difficulty lies in the notion of "copying". If we are going to
> use a method X to derive a conclusion, does it not make sense that X must be
> sound? QM forbids the cloning or copying of states:
>
>  http://en.wikipedia.org/wiki/No_cloning_theorem
>
> "The no cloning theorem is a result of quantum mechanics which forbids the
> creation of identical copies of an arbitrary unknown quantum state. It was
> stated by Wootters, Zurek, and Dieks in 1982, and has profound implications
> in quantum computing and related fields.
>
> The state of one system can be entangled with the state of another system.
> For instance, one can use the Controlled NOT gate and the Walsh-Hadamard
> gate to entangle two qubits. This is not cloning. No well-defined state can
> be attributed to a subsystem of an entangled state. Cloning is a process
> whose end result is a separable state with identical factors.
>
> .....
>
> "No-cloning in a classical context
>
> There is a classical analogue to the quantum no-cloning theorem, which we
> might state as follows: given only the result of one flip of a (possibly
> biased) coin, we cannot simulate a second, independent toss of the same
> coin. The proof of this statement uses the linearity of classical
> probability, and has exactly the same structure as the proof of the quantum
> no-cloning theorem. Thus if we wish to claim that no-cloning is a uniquely
> quantum result, some care is necessary in stating the theorem. One way of
> restricting the result to quantum mechanics is to restrict the states to
> pure states, where a pure state is defined to be one that is not a convex
> combination of other states. The classical pure states are pairwise
> orthogonal, but quantum pure states are not."```
```
But the brain changes from moment to moment due to chemical reactions
and thermal motion and we still remain the same person. If tolerances
were so tight that the no-cloning theorem is relevant then the brain
couldn't possibly function.

--
Stathis Papaioannou

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