On 04-05-2018 01:51, Bruce Kellett wrote:
From: BRENT MEEKER <meeke...@verizon.net>
On 5/3/2018 4:03 PM, Bruce Kellett wrote:
The problem, of course, is that this unitary operator is formed in
the multiverse, so to form its inverse we have to have access to
the other worlds of the multiverse. And this is impossible because
of the linearity of the SE. So although the mathematics of unitary
transformations is perfectly reversible, measurements are not
reversible in principle in the one world we find ourselves to
inhabit.
I think we need a more precise term than "in principle" which could
confuesed with "mathematically". You really mean reversal is
_nomologically_ impossible even though it's _mathematically_
reversible. It's more impossible that _FAPP_ or _statistically_ but
not _logically_ impossible. :-)
Not doable "in principle" just means that there is no conceivable way
in which it could be done. It is not just a matter of difficulty, or
that it would take longer than the lifetime of the universe. It is
actually impossible. Quantum mechanics does not imply that all things
that are logically possible are nomologically possible, or could be
achieved in practice. That is why Saibal's claim that there exists a
unitary operator that does what he wants is rather empty -- there are
an infinite number of unitary operators that are not realizable in
practice. And this limitation is a limitation "in principle".
Bruce
In the QC example by Deutsch, this objection does not apply as all
unitary transforms can be realized. Any unitary transform can be
generated using combinations of the CNOT and the Hadamard gate, so there
is no obstacle to realize the thought experiment, given a large enough
QC.
Saibal
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