Dear Steven,

In your Email you discussed a number of fundamental questions about
relation of QI and CI, and more generally QM and CM. I remark that if
one defines information through entropy than if fact information theory
is reduced to probability theory. Thus the problem of differences
between QI and CI is just a new representation of teh very old problem 
of relation between quantum probability and classical probability. 

Why do we use the Kolmogorov measure-theoretic model everywhere becides
QM? But in QM we should manipulate not with measures but with complex
probability amplitudes? This problem was discussed since 1930th in
hundreds of papers and books. There are two main viewpoints. The first
one can be considered as conventional: \"It is just because NATURE 
behave in such a way!\" 
J. von Neumann pointed out that quatum randomness differs crucially from
classical randomness. Classical randomness is reducible to variety of
properties of systems in ensembles. Quantum randomness is IRREDUCIBLE!

Therefore the main difference between QI and CI is that the first one is
about irreducible randomness, so entropy is not just ENSEMBLE-ENTROPY, 
quantum entropy and hence quantum information are based on irreducible

Why does an electron irreducibly random, but a ball not? The Copenhagen
reply is that because Nature is such. If we follow this line then we
should agree that there should be two different probability theory:
a) Kolmogorov measure-theoretic; b) Quantum -- complex Hilbert space, 
and hence two different information theories: one applied to quantum 
systems and another to classical. 

As was emphasiwed in my previous Email, the main problem of this
(Copenhagen)  approach is that it is not clear which systems should be
considered as quantum and which as classical? Are moleculas irreducibly
or reducibly random? Are cells? Human beings?

As you see, up to now I have not even mentioned so called quantum
nonlocality or entanglement. I shall come back to these problems later.
But I emphasize that they role in the discussion - quantum as opposed to
classical - is overestimated. The difference between classical and
quantum probability and CI and QI was well know long before Bell\'s
theorem. And I think that the real explanation of this difference has
not so much to do with nonlocality (my private viewpoint).

Personally I think that classical and quantum probability and CI and QI
could be unified. I shall soon come with mathematical arguments. At the
moment I pay attention to a purely experimental argument. The
irreducible quantum randomness in experimental framework is always
exhibited through the ensemble randomness!!! This is the fundamental
experimental fact that could not be ignored! We could not demonstrate 
that one fixed photon or electron is \"irreducibly random\" -- we destroy
its state after the first measurement. Therefore for one fixed 
experimental framework we are not able to distinguish \"irreducible
quantum randomness\" and \"reducible classical randomness.\" The problem 
with the classical probabilistic description arises when we conbine the
statistical data from a few different expermental arrangements. 

In particular, this we do in the EPR-Bohm experiment: we should consider 
at least 4 different pairs of settings (directions) for polarization
measurement. However, to see the difference between classical and
quantum probabilistic descriptions we need not consider entangled 
systems. It is enough to consider the two slit experiment for three 
experimental settings: 1) both slits are open; 2) the first slit is open 
and the second is closed; 3) vice versa. If we collect three gistograms,
three probability distributions of particles on the registration screen, 
p_12, p_1, p_2, then we shall see (and this is just an experimental
fact) that in contrast to classical probability theory:
p_12 \\not= [p_1 + p_2]/2 (here the factor 1/2 should appear if we
consider a source of phtonts that is localted syymetrically with respect
to slits). So the classical formular of total probability, by that
it should be that p_12 = [p_1 + p_2]/2 is violated!!! This story is well
described in my book \"Interpretations of Probability\", VSP Int. Publ.,
1999 (second edition 2004). Pay attention that there was nothing about
nonlocality or entanglement, or even composite systems. 

My opinion is that the real problem is not in some distinguishing
features of so called \"quantum systems\", but in combining of statistical
data from a few different experiments. I claim that the same problems
would appear in many other situations where we make such a combining of
data. QM was just the first example. I put this in the mathematical
framework in a series of papers, see e.g.

It was shown that if one operate with CONTEXTUAL PROBABILITIES, so
probability-measures depending on complexes of experimental physical
conditions, then one will not have any problem with quantum 
probabilities. If we choose such a viewpoint then we shall lose all
mysteries of QM and QI. One may find QI-representation for information
corresponding to different contexts (in physics, psychology, chemistry
and so on), see e.g.
on experimental evidences of  quantum_like probabilistic behaviour of 
cognitive systems.

P.S. But if you like nonlocality,  you could proceed with such an
interpretation. There is nothing wrong, since the mathematical apparatus
is correct in any way! 

With Best Regards,
Andrei Khrennikov
Director of International Center for Mathematical Modeling in Physics,
Engineering, Economy and Cognitive Sc.,
University of Vaxjo, Sweden

> Dear Andrei and List,
> I have been reading the session opening post for a few days now and 
> trying to make sense of it in terms of the Foundations of Information
> Science.
> These questions continue to be raised and I am glad the session here
> causes me to return to them.  They continue to be the center of an 
> ongoing crisis in physics.  I am not sure of the state of play - and
> it 
> would be useful to me to have a physicist summarize the latest work. 
> The last paper I reviewed on the subject was James Malley\'s paper 
> (  which, at
> the 
> time, I thought convincingly showed that EPR results do not commute. 
> A 
> paper from Daniele Tommasini 
> ( 
> appears to show that EPR is unmeasurable.  I\'d like to hear the
> standing 
> of these papers today, if anyone knows.
> I was fortunate to be in a conversation with Roger Penrose a few
> years 
> ago about these questions and he put it rather well by saying that he
> was troubled that cricket balls did not appear to behave according to
> the rules of quantum physics. 
> I have a number of standing questions about entanglement theory 
> especially as it related of molecular biology. For example:  Is an 
> entire organism considered to be an entangled entity?  What is the 
> theoretical and experimental justification for stem cells as origin
> of 
> entangled cell structures?  How does that work according to
> entanglement 
> physics?  It is simple to consider entanglement in the case of single
> photons, it is rather more difficult to generalize it.  Although, 
> aggregate manifestations of entanglement may, in fact, be easier to
> deal 
> with both experimentally and theoretically.
> What Penrose is getting at by the above remark is that if such states
> as 
> entanglement/non-locality and superposition do exist at the quantum 
> level they must surely manifest at the classical level.  Andrei\'s
> appeal 
> to scale in his recent post seems unreasonable (he essentially asks
> at 
> what increase of mass entanglement stops). 
> Hence, entangled states/non-locality, superposition, must necessarily
> be 
> in the mechanics of information theory.  In other words, we need a 
> theory of information that unifies classical and quantum theories -
> or 
> we need some reasonable explanation of why there should be two
> theories.
> I think there may, in fact, be ready manifestation of 
> entanglement/non-locality at the classical level underlying the 
> integration of experience in senses. If this is not a classical level
> manifestation of entanglement and non-locality then it requires that
> we 
> do something like Jonathan Edwards\' 
> ( proposal and reduce integrated
> experience to single cells.  This does not seem likely in my view 
> because the argument reduces to a point and if it does not the
> locality 
> issues remain within the cell.  However, I do think Jonathan\'s work
> is 
> very interesting and worthy.  In my view, even if the manifestation
> is 
> isolated to a single cell or just a few cells in the brain, the
> locality 
> issue is a problem for sentience engineering and cognitive science. 
> (Obvious example: smash fingers from both hands in a door. How is it
> you 
> can integrate the pain of each together in a single cognition?) 
> Indeed, I do currently assume in my work that there is this 
> manifestation of entanglement/non-locality at the classical level of
> sentience engineering and that it does explain the integration of 
> experience.  However, whether this non-locality and associated
> sensory / 
> cognitive integration relates directly to EPR I leave as an open 
> question.  There are many miles to go before we sleep.  It certainly
> would be convenient, however, if I could say with some certainty that
> all organisms are entangled entities - in a single whole or in
> parts.
> As to the Toshiba device, as they say here in the USA, \"I\'m from 
> Missouri\" (the \"show me\" state) - I will wait until they actually
> have 
> something to show before passing judgment.
> With respect,
> Steven
> --
> Dr. Steven Ericsson-Zenith
> Andrei Khrennikov (by way of Pedro Marijuan <[EMAIL PROTECTED]>)
> wrote:
> > *11th FIS Discussion Session:
> >
> > *Andrei Khrennikov & Jonathan D.H. Smith
> >
> >
> > *

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