Abstract
We describe a way to transfer informationaldivergences into the nonclassical regime, and statetheir basic properties. This should be seen as a firststep toward a nonclassical estimation theory. Ourprocedure mimics the approach of V. Cantoni in defininga generalized transition probability and only needs areasonable concept of observables (POVmeasures).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Alberti, P.M. (1983). A note on the transition probability over C*-algebras, Letters inMathematical Physics, 7, 25–32.
Alfsen, E. M., and Shultz, F. W. (1976). Non-commutat ive spectral theory for affine function spaces on convex sets, Memoirs of the American Mathematical Society, Vol. 172.
Araki, H. (1976). Relative entropy of states of von Neumann algebras, Publications of the RIMS, 11, 809–833.
Busch, P., Lahti, P., and Mittelstaedt, P. (1991). The Quantum Theory of Measurement, Springer, Berlin.
Cantoni, V. (1975). Generalized “transition probability,” Communications in Mathematical Physics, 44, 125–128.
Gerisch, T., Rieckers, A., and Zanzinger, S. (1996). Operator algebraic transition probabilities in macroscopic quantum systems, preprint.
Gudder, S., Marchand, J.-P., and Wyss, W. (1979). Bures distance and relative entropy, Journal of Mathematical Physics, 20(9), 1963–1966.
Heyer, H. (1982). Theory of Statistical Experiments, Springer, Berlin.
Kosaki, H. (1983). On the Bures distance and the Uhlmann transition probability of states on a von Neumann algebra, Proceedings of the American Mathematical Society, 89, 285.
Liese, F., and Vajda, I. (1985). Convex Statistical Distances, Teubner.
Ohya, M., and Petz, D. (1993). Quantum Entropy and its Use, Springer, Berlin.
Rényi, A. (1961). On measures of entropy and information, in Proceedings of the 1st Berkeley Symposium, Berkeley, Vol. I, pp. 547–561.
Schindler, C. (1991). Representations of state space transformations by Markov kernels, International Journal of Theoretical Physics, 30(11), 1409–1431.
Strătilaă, S. (1981). Modular Theory in Operator Algebras, Abacus Press, Turnbridge Wells.
Zanzinger, S. (1995). Verallgemeinerte Ü bergangswahrscheinl ichkeiten und Quasientropien in der Vielteilchenphysik, Ph.D. thesis, Universität Tübingen.
Rights and permissions
About this article
Cite this article
Zanzinger, S. On Informational Divergences for General Statistical Theories. International Journal of Theoretical Physics 37, 357–363 (1998). https://doi.org/10.1023/A:1026635322144
Issue Date:
DOI: https://doi.org/10.1023/A:1026635322144