Michel Petitjean posted a few fundamental questions about QI, its
applications and its distinguishing features comparing with classical
information.
Michel:
>Physical:
>Apart for electrons, does the QI model is indeed assumed to work for
>any particle or system of particles ?
Andrei: In principle, yes! You could do QI with heavy particles, e.g.,
neutrons. The only restriction to a system is that it should be
\"quantum\". What does it mean? This is the well known problemn of quantum
foundations. At the beginning it was assumed (at least by the
Copenhagen interpretation) that \"quantum\"=\"micro\". Such an agreement was
convenient to exclude such quantum paradoxes, as so called Schrodinger
cat paradox: a macroscopic system in a superposition of two different
states, Schrodinger produced a very natural example of microscopic
superposition which would produce cat in the superposition to be dead
and alive.
Of course, the difficult question of such an interpretation of \"quantum\"
is to find the boundary between micro and macro. So if we increase the
mass of a particle, until which limit it would be still quantum?
Now days the identification \"quantum\"=\"micro\" is not more possible,
since there were observed in real experiments large collective systems,
Bose-Einstein condensate, which exhibit quantum behaviour.
Thus in principle QI might be done even with macroscopic quantum systems.
However, I recall that for real applications even electrons are too
heavy. The real QI will work with photons, since it is easy to transmit
them.
Coming back to the question: Which systems could be considered as
quantum? I remark that one could try to define quantumness via a
special probabilistic behaviour of a system. The basic statistical test
for quantumness of probabilities is INTERFERENCE OF PROBABILITIES. It
can be found for example in the basic two slit experiment.
We can formulate the question about quantumness of macrosystems as the
question of intereference, see \"On the notion of macroscopic quantum
system\", http://www.arxiv.org/abs/quant-ph/0408164
Michel:
>Having two correlated r.v. X1 and X2, the observations of X1
>provide informations about X1, but also about X2.
>What are the basic differences between this kind of correlation and the
>\"correlation\" in the QI case ?
Andrei: In fact, this basic EPR-example with correlated particles was
proposed by people, Einstein, Podolsky and Rosen, who would answer:
There is no any differences between this kind of correlation (namely,
usual classical) and the \"correlation\" in the QI case? For Einstein,
measurements on quantum correlated systems just exhibit correlation
which were present in the initial state. Nowdays it is commonly assumed
(among physicists) taht Einstein was wrong. The reason for such a rather
common opinion is the violation of Bell\'s inequality for correlation for
quantum particles. If one assume that some physical observables (for
example, projections of spin or polarizations of ligh) can be
represented by classical random variables, then correlations SHOULD
satisfy Bell\'s inequality. However, if one make calculations for such
correlations by using quantum formalism, tehn this inequality is
violated! One of the possibilities is that QM simply provides a wrong
model for such experiments. However, teher were done experiments --
by Aspect and then by many others -- and it is commonly assumed that
QM was correct. So the only possibility is to assume that correlations
are NONCLASSICAL.
However, there are two problems with such an interpretation of
violations of Bell\'s inequality;
a). Physical: Experiments were done for photons (even if in textbooks
people write about electrons, nobody was able to do anything with them).
There are huge losses of photons in those experiments. Roughly speaking
for each experiment (for fixed polarizations) we use only a special
and very small part of the ensemble of pairs. This problem is known in
physics as the problem of efficiency of detectors. I do not know another
experiment in any domain of science in that conclusions were based on
such a poor data, see http://www.arxiv.org/abs/quant-ph/0309010
b). Mathematical: It is not well known, but \"Bell\'s inequality\" was used
already by J. Boole (who invented Boolean algebras). He used this
inequality to check whether three random variables can be realized on
the same probability space. He used Boolean algebras, but now days we
can speak about Kolmogorov probability space. The Bell\'s inequality
can be derived only under the assumption that there exists teh common
Kolmogorov probability space for all experimental settings in teh
EPR-experiment: in this inequality there is combined the data from three
different experiments. This is a very strong assumption. If you open
the original book of Kolmogorov on the modern probabilistic axiomatics,
he emphasized that each experimental context generates its own
probability space. In my book \"Interpretations of Probability\", VSP Int.
Publ., Utrecht, 1999
(see also http://www.arxiv.org/abs/quant-ph/0006016)
I explored this point of view and it is easy to see that Bell\'s
inequality can be violated for any context-dependent
collection of measurements.
Conclusion. Personally I am not sure that QI really differs
fundamentally from CI. I would say that it might be that QI is just a
special representation, \"projection\", of CI. But if you like to follow
to the conventional views, you should say: \"Experimental violation of
Bell\'s inequality demonstrated that QM produces nonclassical
correlations.\"
Michel:
>Philosophical:
>Could we say that the entanglement of two particles reduces to the fact
>that a measure done on the first particle indicates something on the
>second particle just because they are interacting ?
Andrei: Einstein and I would say: yes! But the conventional viewpoin:
no! -- because the Bell inequality.
With Best Regards,
Andrei Khrennikov
Director of International Center for Mathematical Modeling in Physics,
Engineering, Economy and Cognitive Sc.,
University of Vaxjo, Sweden
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Received on Thu May 18 16:49:21 2006
