Monotone metrics on matrix spaces

Linear Algebra and Its Applications

Volumn 244, Issue , 1996, Pages 81-96

  Petz, D ^a,b  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030501619     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/0024-3795(94)00211-8     Document Type: Article

References (15)

1. P. M. Alberti and A. Uhlmann, Stochasticity and Partial Order. Doubly Stochastic Maps and Unitary Mixing, VEB Deutscher Verlag Wiss., Berlin, 1981.
2. S. Amari, Differential-Geometrical Methods in Statistics, Lecture Notes in Statist. 28, Springer-Verlag, New York, 1985.
3. T. Ando, Concavity of certain maps and positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26:203-241 (1979).
4. L. L. Campbell, An extended Cencov characterization of the information metric, Proc. Amer. Math. Soc. 98:135-141 (1986).
5. N. N. Cencov, Statistical Decision Rules and Optimal Inferences, Transl. Math. Monogr. 53, Amer. Math. Soc., Providence, 1982.
6. M. D. Choi, Some assorted inequalities for positive linear maps on C*-algebras, J. Operator Theory 4:271-285 (1980).
7. C. Davis, Notions generalizing convexity for functions defined on matrices, in Convexity, Proc. Symp. Pure Math. VII, Amer. Math. Soc., Providence, 1963, pp. 187-202.
8. F. Hansen and G. K. Pedersen, Jensen's inequality for operators and Löwner's theorem, Math. Ann. 258:229-241 (1982).
9. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam, 1982.
10. F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246:205-224 (1980).
11. E. A. Morozova and N. N. Chentsov, Markov invariant geometry on state manifolds (in Russian), Itogi Nauki i Tekhniki 36:69-102 (1990).
12. D. Petz, Quasi-entropies for finite quantum systems, Rep. Math. Phys. 23:57-65 (1986).
13. D. Petz, Geometry of canonical correlation on the state space of a quantum system, J. Math. Phys. 35:780-795 (1994).
14. A. Uhlmann, Density operators as an arena for differential geometry, Rep. Math. Phys. 33:253-263 (1993).
15. H. P. Yuen and M. Lax, Multiple-parameter quantum estimation and measurement of nonselfadjoint observables, IEEE Trans. Inform. Theory IT-19:740-750 (1973).