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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