Brukner–Zeilinger invariant information
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 2, pp. 302-310 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present an alternative interpretation of the notion of invariant information by establishing that it is directly related to the total ordinary variance of a quantum state. Here, "total" means summing the variance over any complete orthogonal set of observables or, equivalently, averaging over a certain sufficiently general ensemble of the observables. This simple, intuitive substratum of the Brukner–Zeilinger invariant information sheds further light on the informational and statistical nature of quantum measurements.
Mots-clés : invariant information
Keywords: quantum measurement, total variance, renormalization.
@article{TMF_2007_151_2_a8,
     author = {Sh. Luo},
     title = {Brukner{\textendash}Zeilinger invariant information},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {302--310},
     year = {2007},
     volume = {151},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a8/}
}
TY  - JOUR
AU  - Sh. Luo
TI  - Brukner–Zeilinger invariant information
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 302
EP  - 310
VL  - 151
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a8/
LA  - ru
ID  - TMF_2007_151_2_a8
ER  - 
%0 Journal Article
%A Sh. Luo
%T Brukner–Zeilinger invariant information
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 302-310
%V 151
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a8/
%G ru
%F TMF_2007_151_2_a8
Sh. Luo. Brukner–Zeilinger invariant information. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 2, pp. 302-310. http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a8/

[1] C. Brukner, A. Zeilinger, Phys. Rev. Lett., 83 (1999), 3354 | DOI | MR | Zbl

[2] C. Brukner, A. Zeilinger, J. Modern Opt., 47 (2000), 2233 ; Phys. Rev. A, 63 (2001), 022113 ; “Information and fundamental elements of the structure of quantum theory”, Time, Quantum, Information, eds. L. Castell, O. Ischebeck, Springer, Berlin, 2003, 323 ; quant-ph/0212084 | DOI | MR | Zbl | DOI | DOI | MR

[3] I. fon Neiman, Matematicheskie osnovy kvantovoi mekhaniki, Nauka, M., 1964 ; A. Wehrl, Rev. Mod. Phys., 50 (1978), 221 | MR | Zbl | DOI | MR

[4] J. Lee, M. S. Kim, Phys. Rev. Lett., 84 (2000), 4236 ; J. Lee, M. S. Kim, C. Brukner, Phys. Rev. Lett., 91 (2003), 087902 | DOI | DOI

[5] J. Rehacek, Z. Hradil, Phys. Rev. Lett., 88 (2002), 130401 ; Z. Hradil, J. Rehacek, Fortschr. Phys., 51 (2003), 150 | DOI | MR | DOI | Zbl

[6] G. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1952 | MR | Zbl

[7] A. Renyi, “On measures of entropy and information”, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I, Univ. California Press, Berkeley, 1961, 547 | MR | Zbl

[8] W. van Dam, P. Hayden, Renyi-entropic bounds on quantum communication, quant-ph/0204093

[9] C. Tsallis, J. Stat. Phys., 52 (1988), 479 ; Braz. J. Phys., 29 (1999), 1 | DOI | MR | Zbl | DOI

[10] E. Simpson, Nature, 163 (1949), 688 | DOI | Zbl

[11] K. S. Lau, Sankhya. Ser. A, 47 (1985), 295 | MR | Zbl

[12] O. Onicescu, C. R. Acad. Sci. Paris, A, 263 (1966), 841 | MR | Zbl

[13] K. Ch. Chatzisavvas, Ch. C. Moustakidis, C. P. Panos, J. Chem. Phys., 123 (2005), 174111 | DOI

[14] V. V. Dodonov, J. Opt. B. Quantum Semiclass. Opt., 4 (2002), S98 ; W. H. Zurek, S. Habib, J. P. Paz, Phys. Rev. Lett., 70 (1993), 1187 ; F. M. Cucchietti, D. A. R. Dalvit, J. P. Paz, W. H. Zurek, Phys. Rev. Lett., 91 (2003), 210403 ; N. Canosa, R. Rossignoli, Phys. Rev. Lett., 88 (2002), 170401 ; T. C. Wei, K. Nemoto, P. M. Goldbart, P. G. Kwiat et. al., Phys. Rev. A, 67 (2003), 022110 ; G. Adesso, F. Illuminati, Phys. Rev. A, 72 (2005), 032334 | DOI | MR | DOI | DOI | DOI | MR | DOI | DOI

[15] E. P. Wigner, Ann. Math., 62 (1955), 548 ; 65 (1957), 203 ; M. L. Mehta, Random matrices, Academic Press, Boston, 1991 | DOI | MR | Zbl | DOI | MR | Zbl | MR | Zbl

[16] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge, 2000 | MR | Zbl

[17] E. P. Wigner, M. M. Yanase, Proc. Natl. Acad. Sci. USA, 49 (1963), 910 ; C. W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, New York, 1976 ; A. S. Holevo, Probabilistic and statistical aspects of quantum theory, North-Holland, Amsterdam, 1982 ; S. Luo, Phys. Rev. Lett., 91 (2003), 180403 ; Proc. Amer. Math. Soc., 132 (2004), 885 ; Phys. Rev. A, 72 (2005), 042110 ; Phys. Rev. A, 73 (2006), 022324 ; Ш.-Л. Луо, ТМФ, 143:2 (2005), 231 ; S. Luo, Q. Zhang, Phys. Rev. A, 69 (2004), 032106 | DOI | MR | Zbl | MR | Zbl | MR | Zbl | DOI | DOI | MR | Zbl | DOI | DOI | MR | MR | Zbl | DOI | MR

[18] R. Jozsa, D. Robb, W. K. Wootters, Phys. Rev. A, 49 (1994), 668 ; S. R. Nichols, W. K. Wootters, Quantum Inf. Comput., 3 (2003), 1 ; G. Mitchison, R. Jozsa, Phys. Rev. A, 69 (2004), 032304 | DOI | MR | MR | Zbl | DOI | MR

[19] L. Brillouin, Science and Information Theory, Academic Press, New York, 1956 | MR | Zbl

[20] J. Wheeler, “Information, physics, quantum: The search for links”, Complexity, Entropy, and Physics of Information (Santa Fe, New Mexico, 1989), ed. W. H. Zurek, Addison-Wesley, Redwood City, CA, 1990, 3 | MR

[21] J. Summhammer, Found. Phys. Lett., 1 (1988), 113 ; Int. J. Theor. Phys., 33 (1994), 171 | DOI | DOI | MR

[22] A. Peres, Quantum Theory: Concepts and Methods, Kluwer, Dordrecht, 1993 | MR | Zbl

[23] B. R. Frieden, B. H. Soffer, Phys. Rev. E, 52 (1995), 2274 ; B. R. Frieden, Science from Fisher Information, A unification, Cambridge Univ. Press, Cambridge, 2004 | DOI | MR | Zbl

[24] M. J. W. Hall, Phys. Rev. A, 59 (1999), 2602 ; 69 (2004), 052113 | DOI | MR | DOI | MR

[25] A. Zeilinger, Found. Phys., 29 (1999), 631 | DOI | MR

[26] C. M. Caves, C. A. Fuchs, R. Schack, Phys. Rev. A, 65 (2002), 022305 | DOI | MR

[27] C. A. Fuchs, J. Modern Opt., 50 (2003), 987 | DOI | MR | Zbl