Distance between states and statistical inference in quantum theory
Annales de l'I.H.P. Physique théorique (1981)
- Volume: 35, Issue: 4, page 287-309
- ISSN: 0246-0211
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topHadjisavvas, N.. "Distance between states and statistical inference in quantum theory." Annales de l'I.H.P. Physique théorique 35.4 (1981): 287-309. <http://eudml.org/doc/76143>.
@article{Hadjisavvas1981,
author = {Hadjisavvas, N.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {distance between two quantal states; statistical inference problem; approximation of a statistical operator; projection postulate},
language = {eng},
number = {4},
pages = {287-309},
publisher = {Gauthier-Villars},
title = {Distance between states and statistical inference in quantum theory},
url = {http://eudml.org/doc/76143},
volume = {35},
year = {1981},
}
TY - JOUR
AU - Hadjisavvas, N.
TI - Distance between states and statistical inference in quantum theory
JO - Annales de l'I.H.P. Physique théorique
PY - 1981
PB - Gauthier-Villars
VL - 35
IS - 4
SP - 287
EP - 309
LA - eng
KW - distance between two quantal states; statistical inference problem; approximation of a statistical operator; projection postulate
UR - http://eudml.org/doc/76143
ER -
References
top- [1] A. Wehrl, Rev. Mod. Phys., t. 50, 1978, p. 221-260. MR496300
- [2] M.B. Ruskai, Ann. Inst. H. Poincaré, t. 19, 1973, p. 357. Zbl0288.46062MR349182
- [3] J. Cyranski, Found. Phys., t. 8, 1978, p. 805. MR495095
- [4] W. Ochs, Rep. Math. Phys., t. 8, 1975, p. 109. MR434290
- [5] A. Uhlmann, Rep. Math. Phys., t. 1, 1970, p. 147. Zbl0209.43101
- [6] R. Ingarden, Rep. Math. Phys., t. 10, 1976, p. 43. Zbl0366.94032
- [7] I. Bialynicki-Birula and J. Mycielski, Comm. Math. Phys., t. 44, 1975, p. 129. MR386550
- [8] E.T. Jaynes, Phys. Rev., t. 106, 1957, p. 620; t. 108, 1957, p. 171. Zbl0084.43701
- [9] N. Hadjisavvas, Ann. Fond. Louis de Broglie, t. 3, 1978, p. 155.
- [10] S. Gudder, J.P. Marchand and W. Wyss, J. Math. Phys., t. 20, 1979, p. 1963. Zbl0425.60095MR546251
- [11] S. Kullback, Information theory and statistics. Wiley, New York, 1959. Zbl0088.10406MR103557
- [12] I. Csiszar, Stud. Scient. Math. Hung., t. 2, 1967, p. 299. Zbl0157.25802
- [13] S. Gudder, Comm. Math. Phys., t. 29, 1973, p. 249. MR342092
- [14] S. Gudder, J.P. Marchand and W. Wyss, J. Math. Phys., t. 20, 1979, p. 1963. Zbl0425.60095MR546251
- [15] V. Cantoni, Comm. Math. Phys., t. 44, 1975, p. 125. MR389088
- [16] S. Gudder, Comm. Math. Phys., t. 63, 1978, p. 265. Zbl0391.60100MR513904
- [17] H. Hadjisavvas, Commun. Math. Phys., 1981 (to be published).
- [18] J.M. Jauch, B. Misra and A.G. Gibson, Helv. Phys. Acta, t. 41, 1968, p. 513. Zbl0179.58303
- [19] B. Misra, in Physical reality and Mathematical description. C. Enz and J. Mehra eds, D. Reidel publishing company, Dortrecht, Holland, 1974. MR465649
- [20] N.S. Kronfli, Int. J. Theor. Phys., t. 3, 1970, p. 191.
- [21] J.M. Jauch, Foundations of Quantum Mechanics. Addisson-Wesley, Reading, Mass, 1968). Zbl0166.23301MR218062
- [22] J. Von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univers. press, Princeton, 1955. Zbl0064.21503
- [23] A.M. Gleason, J. of Rat. mech. and Analysis, t. 6, 1957, p. 885. Zbl0078.28803MR96113
- [24] R. Schatten, Theory of cross-norm spaces, Princeton, 1950.
- [25] N. Hadjisavvas, Lett. math. Phys., t. 5, 1981, p. 327. MR626300
- [26] B. D'Espagnat, Conceptual Foundations of Quantum Mechanics. W. A. Benjamin Inc., 1971.
- [27] N. Hadjisavvas, J. Stat. Phys., t. 26, 1981, p. 693. MR648997
- [28] K. Friedmann and A. Shimony, J. Stat. Phys., t. 3, 1971, p. 301.
- [29] J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, Gauthier-Villars, Paris, 1969. Zbl0175.43801
- [30] I. Singer, Best approximation in normed linear spaces by elements of linear subspaces. Springer Verlag, 1970. Zbl0197.38601MR270044
- [31] I. Singer, The theory of best approximation and functional analysis, S. I. A. M., Philadelphia, 1974. Zbl0291.41020MR374771
- [32] E. Prygovecki, Quantum Mechanics in Hilbert space (Academic Press, 1971). Zbl0217.44204
- [33] K. Bugajska and S. Bugaski, Bull. Acad. Pol. Sci., t. 21, 1976, p. 873.
- [34] E.G. Beltramenti and G. Cassinelli, Riv., Nuov. Cim., t. 6, 1976, p. 321.
- [35] A. Messiah, Mécanique Quantique, Dunod, Paris, 1965. MR129304
- [36] C. Piron, Foundations of Quantum Physics. W. A. Benjamin, Reading, Mass., 1976. Zbl0333.46050MR673578
- [37] N. Hadjisavvas and M. Mugur-Schächter, Lett. Nuovo Cim., t. 23, 1978, p. 439. MR515971
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