-
1
-
-
0001858336
-
On the characterization of the state space in quantum mechanics
-
H. Araki, "On the characterization of the state space in quantum mechanics," Commun. Math. Phys. 75, 1-25 (1980).
-
(1980)
Commun. Math. Phys.
, vol.75
, pp. 1-25
-
-
Araki, H.1
-
2
-
-
0003355631
-
Differential-geometrical methods in statistics
-
Springer, Berlin
-
S. Amari, Differential-geometrical methods in statistics, Lect. Notes Stat. 28 (Springer, Berlin, 1985).
-
(1985)
Lect. Notes Stat.
, vol.28
-
-
Amari, S.1
-
4
-
-
0001945248
-
Dissipation in many-body systems: A geometric approach based on information theory
-
R. Balian, Y. Alhassid, and H. Reinhardt, "Dissipation in many-body systems: A geometric approach based on information theory," Phys. Rep. 131, 1-146 (1986).
-
(1986)
Phys. Rep.
, vol.131
, pp. 1-146
-
-
Balian, R.1
Alhassid, Y.2
Reinhardt, H.3
-
5
-
-
0000519707
-
Statistical distance and the geometry of quantum states
-
S. L. Braunstein and C. M. Caves, "Statistical distance and the geometry of quantum states," Phys. Rev. Lett. 72, 3439-3443 (1994).
-
(1994)
Phys. Rev. Lett.
, vol.72
, pp. 3439-3443
-
-
Braunstein, S.L.1
Caves, C.M.2
-
6
-
-
0002559620
-
Non-commutative extension of the information geometry
-
edited by V. P. Belavkin, O. Hirota, and R. L. Hudson Plenum, New York
-
H. Hasegawa, "Non-commutative extension of the information geometry," in Quantum Communication and Measurement, edited by V. P. Belavkin, O. Hirota, and R. L. Hudson (Plenum, New York, 1995), pp. 327-338.
-
(1995)
Quantum Communication and Measurement
, pp. 327-338
-
-
Hasegawa, H.1
-
7
-
-
36449005102
-
Geometry of canonical correlation on the state space of a quantum system
-
D. Petz, "Geometry of canonical correlation on the state space of a quantum system," J. Math. Phys. 35, 780-795 (1994).
-
(1994)
J. Math. Phys.
, vol.35
, pp. 780-795
-
-
Petz, D.1
-
8
-
-
0001606571
-
The metric Bures and the geometric phase
-
edited by R. Gielerak et al. Kluwer Academic, New York
-
A. Uhlmann, "The metric Bures and the geometric phase," in Groups and Related Topics, edited by R. Gielerak et al. (Kluwer Academic, New York, 1992), pp. 267-274.
-
(1992)
Groups and Related Topics
, pp. 267-274
-
-
Uhlmann, A.1
-
9
-
-
0000381412
-
Density operators as an arena for differential geometry
-
A. Uhlmann, "Density operators as an arena for differential geometry," Rep. Math. Phys. 33, 253-263 (1993).
-
(1993)
Rep. Math. Phys.
, vol.33
, pp. 253-263
-
-
Uhlmann, A.1
-
10
-
-
0009226254
-
Statistical decision rules and optimal inferences
-
American Mathematical Society, Providence
-
N. N. Cencov, Statistical decision rules and optimal inferences. Translation of Math. Monog. 53 (American Mathematical Society, Providence, 1982).
-
(1982)
Translation of Math. Monog.
, vol.53
-
-
Cencov, N.N.1
-
11
-
-
84968505420
-
An extended Čencov characterization of the information metric
-
L. L. Campbell, "An extended Čencov characterization of the information metric," Proc. Am. Math. Soc. 98, 135-141 (1986).
-
(1986)
Proc. Am. Math. Soc.
, vol.98
, pp. 135-141
-
-
Campbell, L.L.1
-
13
-
-
0003233008
-
States, Effects, and Operations
-
Springer, Berlin
-
K. Kraus, States, Effects, and Operations, Lect. Notes Phys. 190 (Springer, Berlin, 1983).
-
(1983)
Lect. Notes Phys.
, vol.190
-
-
Kraus, K.1
-
14
-
-
0002486043
-
Markov invariant geometry on state manifolds
-
in Russian
-
E. A. Morozova and N. N. Chentsov, "Markov invariant geometry on state manifolds," Itogi Nauki Tehniki 36, 69-102 (1990) (in Russian).
-
(1990)
Itogi Nauki Tehniki
, vol.36
, pp. 69-102
-
-
Morozova, E.A.1
Chentsov, N.N.2
-
16
-
-
0002443417
-
On the Riemannian geometry of finite dimensional mixed states
-
J. Dittmann, "On the Riemannian geometry of finite dimensional mixed states," Sem. Sophus Lie 3, 73-87 (1993).
-
(1993)
Sem. Sophus Lie
, vol.3
, pp. 73-87
-
-
Dittmann, J.1
-
17
-
-
0001079995
-
Concavity of certain maps and positive definite matrices and applications to Hadamard products
-
T. Ando, "Concavity of certain maps and positive definite matrices and applications to Hadamard products," Lin. Alg. Appl. 26, 203-241 (1979).
-
(1979)
Lin. Alg. Appl.
, vol.26
, pp. 203-241
-
-
Ando, T.1
-
18
-
-
0003316037
-
Jensen's inequality for operators and Löwner's theorem
-
F. Hansen and G. K. Pedersen, "Jensen's inequality for operators and Löwner's theorem," Math. Ann. 258, 229-241 (1982).
-
(1982)
Math. Ann.
, vol.258
, pp. 229-241
-
-
Hansen, F.1
Pedersen, G.K.2
-
19
-
-
0002988067
-
Quasi-entropies for finite quantum systems
-
D. Petz, "Quasi-entropies for finite quantum systems," Rep. Math. Phys. 21, 57-65 (1986).
-
(1986)
Rep. Math. Phys.
, vol.21
, pp. 57-65
-
-
Petz, D.1
-
20
-
-
0347725868
-
Monotone metrics on matrix spaces
-
to appear
-
D. Petz, "Monotone metrics on matrix spaces," Lin. Alg. Appl. (to appear).
-
Lin. Alg. Appl.
-
-
Petz, D.1
-
21
-
-
0000472839
-
Means of positive linear operators
-
F. Kubo and T. Ando, "Means of positive linear operators," Math. Ann. 246, 205-224 (1980).
-
(1980)
Math. Ann.
, vol.246
, pp. 205-224
-
-
Kubo, F.1
Ando, T.2
-
22
-
-
0345834084
-
Curvature in the geometry of canonical correlation
-
to appear
-
F. Hiai, D. Petz, and G. Toth, "Curvature in the geometry of canonical correlation," Studia Sci. Math. Hung, (to appear).
-
Studia Sci. Math. Hung
-
-
Hiai, F.1
Petz, D.2
Toth, G.3
-
23
-
-
84968519073
-
Some convexity and subadditivity properties of entropy
-
E. H. Lieb, "Some convexity and subadditivity properties of entropy," Bull. Am. Math. Soc. 81, 1-14 (1975).
-
(1975)
Bull. Am. Math. Soc.
, vol.81
, pp. 1-14
-
-
Lieb, E.H.1
-
24
-
-
85045503074
-
On the Riemannian metric of α-entropies of density matrices
-
to be published
-
D. Petz and H. Hasegawa "On the Riemannian metric of α-entropies of density matrices," to be published in Lett. Math. Phys
-
Lett. Math. Phys
-
-
Petz, D.1
Hasegawa, H.2
-
26
-
-
0004341311
-
-
Interscience, Wiley, New York
-
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Volume I (Interscience, Wiley, New York, 1963).
-
(1963)
Foundations of Differential Geometry
, vol.1
-
-
Kobayashi, S.1
Nomizu, K.2
-
27
-
-
0002474690
-
Equiprobability, inference and entropy in quantum theory
-
R. Balian and N. L. Balazs, "Equiprobability, inference and entropy in quantum theory," Ann. Phys. 179, 97-144 (1986).
-
(1986)
Ann. Phys.
, vol.179
, pp. 97-144
-
-
Balian, R.1
Balazs, N.L.2
|