Stathis Papaioannou wrote:
On 24 April 2015 at 11:27, Bruce Kellett <[email protected]> wrote:
LizR wrote:
But there's no-cloning to consider - plus whether a simulated quantum
state is the same as a real one...
No-cloning of an unknown quantum state is simply the statement that there is
no unitary operator that will enable you to transfer the properties of one
unknown quantum state to another.
Simulating a quantum state might be another matter. Quantum states are
generally described in terms of some basis in Hilbert space. The
coefficients of the expansion in that basis are arbitrary complex numbers,
subject to the usual normalization conventions for the state. If you want to
simulate this state, you have to simulate these coefficients to arbitrary
precision. This is not possible in finite time with a digital computer.
However, if an infinite number of calculations are routinely possible for a
Turing machine in Platonia, then who knows?
I will give my proof that these coefficients are indeed dense in the complex
plane at a later time, if required.
The inability to clone a particular quantum state at will does not
mean a copy of the quantum state cannot exist, and in fact in a large
enough universe it will exist, without anyone putting any effort into
creating it. But it is unreasonable to insist that a copy of a brain
must be identical to the quantum level when in ordinary life our
brains undergo gross (compared to the quantum level) changes, and we
feel that we survive.
The existence of another identical quantum state may well be possible,
but it can never be proved that /this/ quantum state is identical to
/that/ state when both are generic unknown states.
I don't think this has anything to do with the brain or consciousness.
All is really demonstrates is that the universe as a whole is not Turing
emulable -- but we probably knew that anyway.
Bruce
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