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 randomness. 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. http://www.arxiv.org/abs/quant-ph/0302194 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. http://www.arxiv.org/abs/quant-ph/0307201 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 > (http://arxiv.org/ftp/quant-ph/papers/0402/0402126.pdf) which, at > the > time, I thought convincingly showed that EPR results do not commute. > A > paper from Daniele Tommasini > (http://philsci-archive.pitt.edu/archive/00000651/00/locaqft.pdf) > 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\' > (http://www.ucl.ac.uk/~regfjxe/aw.htm) 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 > SEMEIOSIS RESEARCH > INSTITUTE for ADVANCED SCIENCE & ENGINEERING > > http://www.semeiosis.org > http://iase.info > > > Andrei Khrennikov (by way of Pedro Marijuan <[EMAIL PROTECTED]>) > wrote: > > *11th FIS Discussion Session: > > > > **QUANTUM INFORMATION* > > *Andrei Khrennikov & Jonathan D.H. Smith > > > > > > * > _______________________________________________ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
