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2008 | 6 | 2 | 363-371

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The uncertainty relation expressed by means of a new entropic function


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In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.


  • Institute of Mathematics, Slovak Academy of Sciences, SK-814 73, Bratislava, Štefánikova 49, Slovak Republic


  • [1] V. Majerník, E. Majerníková, S. Shpyrko, Cent. Eur. J. Phys. 3, 393 (2003) http://dx.doi.org/10.2478/BF02475852[Crossref]
  • [2] I. Vajda, Theory of Statistical Inference and Information (Kluwer Academic Publishers, Dortrecht, 1996)
  • [3] I. Csiszár, Publ. Math. Inst. Hungar. Acad. Sci. 8, 85 (1963)
  • [4] S. Kullback, R.A. Leibler, Annals Mathematical Statistics 22, 79 (1951) http://dx.doi.org/10.1214/aoms/1177729694[Crossref]
  • [5] Z. Daróczy, MTA III. Osztály Közleménzyei, 19, 11 (1969) (in Hungarian)
  • [6] J. Aczcél, Z. Daróczy, On measures of information and their characterizations (New York, Academic Press, 1972)
  • [7] F. Österreicher, Ciszár’s f-divergences-Basic Properties, Preprint of Institute of Mathematics of University of Saltzburg (2002)
  • [8] A. Rényi, On the Measures of Entropy and Information, In: 4th Berkeley Symp. Math. Stat. Probability 1, 541 (1961)
  • [9] A. Bhattacharyya, Sankhya 8, 1 (1946)
  • [10] H. Chernoff, An. Math. Stat. 30, 493 (1952) http://dx.doi.org/10.1214/aoms/1177729330[Crossref]
  • [11] W. Finkel, Phys. Rev. A 35, 1488 (1987) http://dx.doi.org/10.1103/PhysRevA.35.1486[Crossref]
  • [12] V. Majerník, L. Richterek, Eur. J. Phys. 18, 73 (1997) http://dx.doi.org/10.1088/0143-0807/18/2/005[Crossref]
  • [13] B. Mamojka, Int. J. Theor. Phys. 11, 73 (1974) http://dx.doi.org/10.1007/BF01811035[Crossref]
  • [14] M. Portesi, A. Plastino, Physica A 225, 411 (1996) http://dx.doi.org/10.1016/0378-4371(95)00475-0[Crossref]
  • [15] V. Majerník, Int. J. Gen. Syst. 33, 673 (2004) http://dx.doi.org/10.1080/03081070410001723139[Crossref]
  • [16] J. Havrda, F. Charvat, Kybernetika 3, 30 (1967)
  • [17] D. Morales, L. Padro, I. Vajda, IEEE Trans. on Syst., Man, and Cyber, Part A: Systems and Humans 26, 681 (2006) http://dx.doi.org/10.1109/3468.541329[Crossref]

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