Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Bures distance and the Uhlmann transition probability of states on a von Neumann algebra


Author: Hideki Kosaki
Journal: Proc. Amer. Math. Soc. 89 (1983), 285-288
MSC: Primary 46L30
DOI: https://doi.org/10.1090/S0002-9939-1983-0712638-2
MathSciNet review: 712638
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Simple expressions for the Bures distance and the Uhlmann transition probability of states on a von Neumann algebra are obtained. Based on these expressions, certain properties are immediately derived.


References [Enhancements On Off] (What's this?)

  • [1] H. Araki, Positive cones, Radon-Nikodym theorems, relative Hamiltonian and Gibbs condition in statistical mechanics ($ {C^*}$-Algebras and their Applications to Statistical Mechanics and Quantum Field Theory (D. Kastler, ed.), North-Holland, Amsterdam, 1976. MR 0675642 (58:32670)
  • [2] H. Araki and G. Raggio, A remark on transition probability, Lett. Math. Phys. 6 (1982), 237-240. MR 660213 (83k:46052)
  • [3] D. Bures, An extension of Kakutani's theorem on infinite product measures to the tensor product of semifinite von Neumann algebras, Trans. Amer. Math. Soc. 135 (1969), 199-212. MR 0236719 (38:5014)
  • [4] S. Gudder, J. P. Marchand and W. Wyss, Bures distance and relative entropy, J. Math. Phys. 20 (1979), 1963-1966. MR 546251 (80j:46109)
  • [5] J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, Gauthier-Villars, Paris, 1969.
  • [6] -, Les $ {C^*}$-algèbres et leurs représentations, Gauthier-Villars, Paris, 1969. MR 0246136 (39:7442)
  • [7] N. Hadjisavvas, On Catoni's generalized transition probability, Comm. Math. Phys. 83 (1982), 43-48. MR 648357 (83d:81035)
  • [8] A. Uhlmann, The "transition probability" in the state space of a $ ^*$-algebra, Rep. Math. Phys. 9 (1976), 273-279. MR 0423089 (54:11072)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L30

Retrieve articles in all journals with MSC: 46L30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0712638-2
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society