Abstract
We examine the problem of the existence (in classical and/or quantum physics) of longitudinal limitations of measurability, defined as limitations preventing the measurement of a given quantity with arbitrarily high accuracy. We consider a measuring device as a generalized communication system, which enables us to use methods of information theory. As a direct consequence of the Shannon theorem on channel capacity, we obtain an inequality which limits the accuracy of a measurement in terms of the average power necessary to transmit the information content of the measurement itself. This inequality holds in a classical as well as in a quantum framework.
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References
L. Szilard, Z. Phys. 53, 840 (1929); R. P. Poplavskiî, Uspekhi Fiz. Nauk 128, 165 (1979).
H. Reichenbach, Philosophische Grundlagen der Quantenmechanik (Birkhäuser Verlag, Basel, 1949), p. 14; J. P. Gordon and W. H. Louisell, in Physics of Quantum Electronics, P. L. Kelley, B. Lax, and P. E. Tannenwald, eds. (McGraw-Hill, New York, 1966), pp. 833–840; V. Majernik, Commun. Math. Phys. 12, 233 (1969);Acta Phys. Austr. 31, 271 (1970).
L. Brillouin, Science and Information Theory, 2nd ed. (Academic Press, New York, 1971).
C. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1972); R. M. Fano, Nuovo Cimento Suppl. 31, 359 (1959).
S. Goldmann, Information Theory (Dover, New York, 1968).
V. Majernik, Acta Phys. Austr. 25, 243 (1967).
J. Cyranski, Found. Phys. 8, 805 (1978).
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D'Antonl, C., Scanzano, P. An application of information theory: Longitudinal measurability bounds in classical and quantum physics. Found Phys 10, 875–885 (1980). https://doi.org/10.1007/BF00708686
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DOI: https://doi.org/10.1007/BF00708686