Abstract
We use a class of generalized relative entropies on density matrices to obtain one-parameter families of torsion-free affine connections.
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REFERENCES
Amari, S. (1985). Differential-geometrical methods in statistic, Lecture Notes in Statistics, Vol. 28.
Amari, S., Barndorff-Nielsen, O. E., Kass, R. E., Lauritzen, S. L., and Rao, C. R. (1987). Differential geometry in statistical inference, IMS Lecture notes-Monograph series, Vol. 10.
Chentsov, N. N. (1982). Statistical decision rules and optimal inferences, Translation of Mathematical Monograph 53, American Mathematical Society, Providence.
Chentsov, N. N. and Morozova, E. A. (1990). Markov invariant geometry on state manifolds, Itogi Nauki i Tekhniki 36, 69-102, (in Russian).
Eguchi, S. (1983). Second order efficiency of minimum contrast estimation in a curved exponential family, Annals of Statistics 11, 793-803.
Hasegawa, H. (1993). α-divergence of the non-commutative information geometry, Reports on Mathematical Physics 33, 87-93.
Jenčovä, A. (2001). Geometry of quantum states: dual Connections and divergence functions. Reports on Mathematical Physics 47, 121-138.
Jenčoväa, A. (2001). Dualistic properties of the manifold of quantum states. In Disordered and Complex Systems, P. Sollich et al., eds., AIP, Melville, New York.
Lesniewski, L. and Ruskai, M. B. (1999). Monotone Riemannian metrics and relative entropy on noncommutative probability spaces, Journal of Mathematical Physics 40, 5702-5724.
Nagaoka, H. (1994). Differential geometrical aspects of quantum state estimation and relative entropy. In Quantum Communication, Computing and Measurement, Hirota et al., eds., Plenum Press
Petz, D. (1986). Quasi-entropies for finite quantum systems. Reports on Mathematical Physics 23, 57-65.
Petz, D. (1994). Geometry of canonical correlation on the state space of a quantum system. Journal of Mathematical Physics 244, 780-795.
Petz, D. (1996). Monotone metrics on matrix spaces, Linear Algebra and its Applications 244, 81-96.
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Jenčová, A. Generalized Relative Entropies as Contrast Functionals on Density Matrices. International Journal of Theoretical Physics 43, 1635–1649 (2004). https://doi.org/10.1023/B:IJTP.0000048809.54756.84
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DOI: https://doi.org/10.1023/B:IJTP.0000048809.54756.84