Re: BIT from QUBIT?

From: Bruno Marchal <>
Date: Thu, 22 Aug 2002 16:41:04 +0200

Hi Stephen,

>You mind want to read and consider the implications of this paper and
>related ones:

I did not know this reference, but I knew Svozil works. I appreciate
two of his books. His approach is interesting and perhaps dual to
some aspect of mine.
To summarize, in my approach "we" are duplicated all the time but
cannot know it, and the quantum emerges from that. In Svozil-Conway-Moore
partition logics, the object of study is a black box automaton which cannot
be duplicated, and cannot be opened, and the quantum emerges from that.
The approach are perhaps related. I don't know.

> The key passage in it is:
>As might have been suspected, it turns out that, in order to be able to
>perform the mapping from the quantum universe into the classical one
>consistently, important structural elements of the quantum universe have to
>be sacrificed:

 From this you can read QUBIT cannot be obtained from BIT ... by the sort
of mapping he describes in the paper.
In my approach there is no mapping of this sort, so that result does
not apply.
Apparently the approach of Svozil & Al generalizes Kochen-Specker form
of no go theorems. This is not at all how I proceed.

>Svozil & Al: Since per definition, the quantum propositional calculus is
>nondistributive (nonboolean), a straightforward embedding which preserves
>all the logical operations among observables, irrespective of whether or not
>they are co-measurable, is impossible. This is due to the quantum mechanical
>feature of complementarity.

I agree with this of course.

>Svozil & Al: One may restrict the preservation of the logical
>operations to be valid only among mutually orthogonal propositions.
>In this case it turns out that
>again a consistent embedding is impossible, since no consistent meaning can
>be given to the classical existence of ``counterfactuals.'' This is due to
>the quantum mechanical feature of contextuality. That is, quantum
>observables may appear different, depending on the way by which they were
>measured (and inferred).


>Svozil & Al: In a further step, one may abandon preservation of
>lattice operations such
>as not and the binary and and or operations altogether. One may merely
>require the preservation of the implicational structure (order relation). It
>turns out that, with these provisos, it is indeed possible to map quantum
>universes into classical ones. Stated differently, definite values can be
>associated with elements of physical reality, irrespective of whether they
>have been measured or not. In this sense, that is, in terms of more
>``comprehensive'' classical universes (the hidden parameter models), quantum
>mechanics can be ``understood.''
> ***
>Stephen Paul King Am I mistaken in my understanding that this
>implies BIT /subset QuBIT
>and NOT QUBIT /subset BIT?

Well in the last paragraph, as I understand it, the authors seems to say
that qubits *can* be subset of bits. But then it appears that the injective
mapping for that embedding does no more preserve any lattice operations
except the implicational structure. But this follows immediately, it seems
to me, by the fact that a classical universal turing machine can simulate any
quantum turing machine.

Mmmh... Now I see the limitations of the QUBIT/BIT rephrasing of the mind-body
problem :(

Best regards,

Received on Thu Aug 22 2002 - 07:47:24 PDT

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