From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 4 May 2018, at 01:03, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
Actually, this is the basis of MWI -- everything in physics is based
on unitary transformations. The Schrödinger equation can be derived
by assuming time evolution is unitary. So, in the wider context,
everything, even decoherence into the wider universe, is reversible,
in the sense that there is a unitary transformation that, when
applied to any final state, restores the initial state -- just take
the unitary operator that describes the time evolution, say U, and
then take its inverse, U^{-1}.
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.
So even Deutsch's quantum brain is likely to run into difficulties,
since it has to communicate with the real world.
OK. But that is the same with any quantum computer. Are you saying
that quantum computing is not possible in practice?
No, quantum computing should be possible with sufficient protection
against decoherence.
There are quantum algorithm capable of “fighting by quantum error
procedures” the effect of decoherence. Imo, the Deutsch experiment is
as much possible as a working quantum computer. I am pretty sure this
is technologically possible, although plausibly not even in a near
future, but soon after :)
The problem with Deutsch's thought experiment is that everything takes
place within the quantum computer, so no real measurement has ever been
made. Measurement involves decoherence and the effectively permanent
splitting of branches. No quantum computer can work in such
circumstances. Calling the unmeasured elements of a superposition
"worlds" as Deutsch does, equivocates on the orthogonality inherent in
an operational concept of a "world". If elements of a superposition can
interfere, they are not separate worlds. Deutsch's idea is sunk by the
"preferred basis" problem. It is only decoherence into the external
world that can fix the basis (by einselection).
Bruce
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