-
1
-
-
79958810366
-
Operator log-convex functions and operator means
-
Zbl 1227098 MR 2805638
-
T. Ando and F. Hiai, Operator log-convex functions and operator means, Math. Ann. 350 (2011), 611-630. Zbl 1227098 MR 2805638
-
(2011)
Math. Ann
, vol.350
, pp. 611-630
-
-
Ando, T.1
Hiai, F.2
-
2
-
-
85008097854
-
Relative entropy of states of von Neumann algebras
-
Zbl 0326.46031 MR 0425631
-
H. Araki, Relative entropy of states of von Neumann algebras, Publ. RIMS Kyoto Univ. 11 (1976), 809-833. Zbl 0326.46031 MR 0425631
-
(1976)
Publ. RIMS Kyoto Univ
, vol.11
, pp. 809-833
-
-
Araki, H.1
-
3
-
-
0000489740
-
Information-type measures of difference of probability distributions and indirect observations
-
Zbl 0157.25802 MR 0219345
-
I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar. 2 (1967), 299-318. Zbl 0157.25802 MR 0219345
-
(1967)
Studia Sci. Math. Hungar
, vol.2
, pp. 299-318
-
-
Csiszár, I.1
-
4
-
-
59049088495
-
A matrix convexity approach to some celebrated quantum inequalities
-
USA, Zbl 1202.81018 MR 2475796
-
E. G. Effros, A matrix convexity approach to some celebrated quantum inequalities, Proc. Nat. Acad. Sci. USA 106 (2009), 1006-1008. Zbl 1202.81018 MR 2475796
-
(2009)
Proc. Nat. Acad. Sci
, vol.106
, pp. 1006-1008
-
-
Effros, E.G.1
-
5
-
-
0035628303
-
Uniqueness of the Chentsov metric in quantum information theory
-
Zbl 1039.81011 MR 1841616
-
M. Grasselli and R. F. Streater, Uniqueness of the Chentsov metric in quantum information theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4 (2001), 173-182. Zbl 1039.81011 MR 1841616
-
(2001)
Infin. Dimens. Anal. Quantum Probab. Relat. Top
, vol.4
, pp. 173-182
-
-
Grasselli, M.1
Streater, R.F.2
-
6
-
-
33748055212
-
Characterizations of symmetric monotone metrics on the state space of quantum systems, Quantum Inform
-
Zbl 1152.81729 MR 2298673
-
F. Hansen, Characterizations of symmetric monotone metrics on the state space of quantum systems, Quantum Inform. Comput. 6 (2006), 597-605. Zbl 1152.81729 MR 2298673
-
(2006)
Comput
, vol.6
, pp. 597-605
-
-
Hansen, F.1
-
7
-
-
85157280520
-
-
Zbl 1157.47305 MR 2256619
-
F. Hansen, Extensions of Lieb's concavity theorem, J. Statist. Phys. 124 (2006), Zbl 1157.47305 MR 2256619
-
(2006)
J. Statist. Phys
-
-
Hansen, F.1
-
8
-
-
0003316037
-
Jensen's inequality for operators and Löwner's theorem
-
Zbl 0473.47011 MR 1513286
-
F. Hansen and G. K. Pedersen, Jensen's inequality for operators and Löwner's theorem, Math. Ann. 258 (1982), 229-241. Zbl 0473.47011 MR 1513286
-
(1982)
Math. Ann
, vol.258
, pp. 229-241
-
-
Hansen, F.1
Pedersen, G.K.2
-
9
-
-
11044227082
-
Means of Hilbert space operators
-
1820, Springer, Zbl 1048.47001 MR 2005250
-
F. Hiai and H. Kosaki, Means of Hilbert space operators, Lecture Notes in Math. 1820, Springer, 2003. Zbl 1048.47001 MR 2005250
-
(2003)
Lecture Notes In Math
-
-
Hiai, F.1
Kosaki, H.2
-
10
-
-
80052040382
-
Quantum f -divergences and error correction
-
Zbl 1230.81007 MR 2826462
-
F. Hiai, M. Mosonyi, D. Petz and C. Bény, Quantum f -divergences and error correction, Rev. Math. Phys. 23 (2011), 691-747. Zbl 1230.81007 MR 2826462
-
(2011)
Rev. Math. Phys
, vol.23
, pp. 691-747
-
-
Hiai, F.1
Mosonyi, M.2
Petz, D.3
Bény, C.4
-
11
-
-
0005232902
-
Sufficiency, KMS condition and relative entropy in von Neumann algebras
-
Zbl 0473.46044 MR 0634765
-
F. Hiai, M. Ohya and M. Tsukada, Sufficiency, KMS condition and relative entropy in von Neumann algebras, Pacific J. Math. 96 (1981), 99-109. Zbl 0473.46044 MR 0634765
-
(1981)
Pacific J. Math
, vol.96
, pp. 99-109
-
-
Hiai, F.1
Ohya, M.2
Tsukada, M.3
-
14
-
-
77958563426
-
A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality
-
Zbl 1218.81025 MR 2733251
-
A. Jenčová and M. B. Ruskai, A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality, Rev. Math. Phys. 22 (2010), 1099-1121. Zbl 1218.81025 MR 2733251
-
(2010)
Rev. Math. Phys
, vol.22
, pp. 1099-1121
-
-
Jenčová, A.1
Ruskai, M.B.2
-
15
-
-
0000472839
-
Means of positive linear operators
-
Zbl 0412.47013 MR 0563399
-
F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246 (1980), 205-224. Zbl 0412.47013 MR 0563399
-
(1980)
Math. Ann
, vol.246
, pp. 205-224
-
-
Kubo, F.1
Ando, T.2
-
16
-
-
78049433035
-
A characterization of extended monotone metrics
-
Zbl 1206.94016 MR 2737244
-
W. Kumagai, A characterization of extended monotone metrics, Linear Algebra Appl. 434 (2011), 224-231. Zbl 1206.94016 MR 2737244
-
(2011)
Linear Algebra Appl
, vol.434
, pp. 224-231
-
-
Kumagai, W.1
-
17
-
-
0033240088
-
Monotone Riemannian metrics and relative entropy on noncommutative probability spaces
-
Zbl 0968.81006, MR 1722334
-
A. Lesniewski and M. B. Ruskai, Monotone Riemannian metrics and relative entropy on noncommutative probability spaces, J. Math. Phys. 40 (1999), 5702-5724. Zbl 0968.81006 MR 1722334
-
(1999)
J. Math. Phys
, vol.40
, pp. 5702-5724
-
-
Lesniewski, A.1
Ruskai, M.B.2
-
18
-
-
36649022319
-
Convex trace functions and the Wigner-Yanase-Dyson conjecture
-
Zbl 0267.46055 MR 0332080
-
E. H. Lieb, Convex trace functions and the Wigner-Yanase-Dyson conjecture, Adv. Math. 11 (1973), 267-288. Zbl 0267.46055 MR 0332080
-
(1973)
Adv. Math
, vol.11
, pp. 267-288
-
-
Lieb, E.H.1
-
19
-
-
0000411043
-
Some operator inequalities of the Schwarz type
-
Zbl 0274.46045 MR 0336406
-
E. H. Lieb and M. B. Ruskai, Some operator inequalities of the Schwarz type, Adv. Math. 12 (1974), 269-273. Zbl 0274.46045 MR 0336406
-
(1974)
Adv. Math
, vol.12
, pp. 269-273
-
-
Lieb, E.H.1
Ruskai, M.B.2
-
20
-
-
33947426775
-
On divergences and informations in statistics and information theory
-
MR 2300826
-
F. Liese and I. Vajda, On divergences and informations in statistics and information theory, IEEE Trans. Inform. Theory 52 (2006), 4394-4412. MR 2300826
-
(2006)
IEEE Trans. Inform. Theory
, vol.52
, pp. 4394-4412
-
-
Liese, F.1
Vajda, I.2
-
21
-
-
84967493898
-
On Fisher information on quantum statistical models
-
Hayashi (ed.)
-
H. Nagaoka, On Fisher information on quantum statistical models, in Asymptotic theory of quantum statistical inference, M. Hayashi (ed.), World Sci., 2005, 113-124.
-
(2005)
World Sci
, pp. 113-124
-
-
Nagaoka, H.1
-
23
-
-
85008571251
-
Quasi-entropies for states of a von Neumann algebra
-
Zbl 0606.46039 MR 0817164
-
D. Petz, Quasi-entropies for states of a von Neumann algebra, Publ. RIMS Kyoto Univ. 21 (1985), 787-800. Zbl 0606.46039 MR 0817164
-
(1985)
Publ. RIMS Kyoto Univ
, vol.21
, pp. 787-800
-
-
Petz, D.1
-
24
-
-
85157216375
-
-
Zbl 0629.46061 MR 0868631
-
D. Petz, Quasi-entropies for finite quantum systems, Rep. Math. Phys. 23 (1986), Zbl 0629.46061 MR 0868631.
-
(1986)
Rep. Math. Phys
, vol.23
-
-
Petz, D.1
-
25
-
-
36449005102
-
-
D. Petz, Geometry of canonical correlation on the state space of a quantum system, Zbl 0804.53101 MR 1257547
-
D. Petz, Geometry of canonical correlation on the state space of a quantum system, J. Math. Phys. 35 (1994), 780-795. Zbl 0804.53101 MR 1257547.
-
(1994)
J. Math. Phys
, vol.35
, pp. 780-795
-
-
Petz, D.1
-
26
-
-
0030501619
-
Monotone metrics on matrix spaces
-
Zbl 0856.15023 MR 1403277
-
D. Petz, Monotone metrics on matrix spaces, Linear Algebra Appl. 244 (1996), 81-96. Zbl 0856.15023 MR 1403277
-
(1996)
Linear Algebra Appl
, vol.244
, pp. 81-96
-
-
Petz, D.1
-
27
-
-
0042383302
-
-
Covariance and Fisher information in quantum mechanics, Zbl 1168.81317 MR 1890135
-
D. Petz, Covariance and Fisher information in quantum mechanics, J. Phys. A 35 (2002), 929-939. Zbl 1168.81317 MR 1890135.
-
(2002)
J. Phys. A
, vol.35
, pp. 929-939
-
-
Petz, D.1
-
28
-
-
85157072407
-
-
Quantum information theory and quantum statistics, Springer, Berlin, Zbl 1145.81002 MR 2363070
-
D. Petz, Quantum information theory and quantum statistics, Springer, Berlin, 2008. Zbl 1145.81002 MR 2363070.
-
(2008)
-
-
Petz, D.1
-
29
-
-
77953486352
-
From f -divergence to quantum quasi-entropies and their use
-
D. Petz, From f -divergence to quantum quasi-entropies and their use, Entropy 12 (2010), 304-325. Zbl 1229.81054 MR 2608239.
-
(2010)
Entropy
, vol.12
, pp. 304-325
-
-
Petz, D.1
-
30
-
-
84866852848
-
Introduction to quantum Fisher information
-
R. Rebolledo and M. Ország (eds.), World Sci., Zbl pre06042766 MR 2799128
-
D. Petz and C. Ghinea, Introduction to quantum Fisher information, in Quantum probability and related topics, QP-PQ: Quantum Probab. White Noise Anal. 27, R. Rebolledo and M. Ország (eds.), World Sci., 2011, 261-281. Zbl pre06042766 MR 2799128
-
(2011)
Quantum Probability and Related Topics, QP-PQ: Quantum Probab. White Noise Anal
, vol.27
, pp. 261-281
-
-
Petz, D.1
Ghinea, C.2
-
31
-
-
0005231842
-
Convexity inequalities for estimating free energy and relative entropy
-
Zbl 0709.60549 MR 1063572
-
M. B. Ruskai and F. H. Stillinger, Convexity inequalities for estimating free energy and relative entropy, J. Phys. A 23 (1990), 2421-2437. Zbl 0709.60549 MR 1063572
-
(1990)
J. Phys. A
, vol.23
, pp. 2421-2437
-
-
Ruskai, M.B.1
Stillinger, F.H.2
-
33
-
-
0005180661
-
Information content of distributions
-
Zbl 0128.14104 MR 0151127
-
E. P. Wigner and M. M. Yanase, Information content of distributions, Proc. Nat. Acad. Sci. USA 49 (1963), 910-918. Zbl 0128.14104 MR 0151127
-
(1963)
Proc. Nat. Acad. Sci. USA
, vol.49
, pp. 910-918
-
-
Wigner, E.P.1
Yanase, M.M.2
|