2010

From quasi-entropy

Petz, Denes

Understand

The subject is the overview of the use of quasi-entropy in finite dimensional spaces.

Matrix monotone functions and relative modular operators are used.
The origin is the relative entropy and the f-divergence, monotone metrics, covariance and the chi-square-divergence are the most important particular cases.
The extension of the monotone metric to two variables is a new concept.

Built on

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Similar

M.B. Ruskai and F.H. Stillinger, Convexity inequalities for estimating free energy and relative entropy, J. Phys. A 23, 2421–2437 (1990)
1990
Cited alongside, same era.
D. Petz, Geometry of canonical correlation on the state space of a quantum system, J. Math. Phys. 35
1994
Cited alongside, same era.
D. Petz, Monotone metrics on matrix spaces, Linear Algebra Appl. 244
1996
Cited alongside, same era.
A. Lesniewski and M.B. Ruskai, Monotone Riemannian metrics and relative entropy on noncommutative probability spaces, J. Math. Phys. 40
1999
Cited alongside, same era.
M. Grasselli and R.F. Streater, Uniqueness of the Chentsov metric in quantum information theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 4
2001
Cited alongside, same era.
D. Petz, Covariance and Fisher information in quantum mechanics. J. Phys. A: Math. Gen. 35
2003
Cited alongside, same era.
M. Ohya and D. Petz, Quantum Entropy and Its Use
2004
Cited alongside, same era.
H. Nagaoka, On Fisher information on quantum statistical models, in Asymptotic Theory of Quantum Statistical Inference
2005
Cited alongside, same era.
F. Hiai, M. Mosonyi and D. Petz, Monotonicity of f f -divergences: A review with new results, arXiv:1008.2529
Original
Cited in the paper.
A. Jenčová and M.B. Ruskai, A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality, arXiv:0903.2895
Original
Cited in the paper.
W. Kumagai, A characterization of extended monotone metrics, to be published in Lin. Alg. Appl
Cited in the paper.
K. Temme, M. J. Kastoryano, M. B. Ruskai, M. M. Wolf and F. Verstraete, The χ 2 \chi^{2} -divergence and mixing times of quantum Markov processes, arXiv:1005.2358
Original
Cited in the paper.

Then

F. Hansen, Characterizations of symmetric monotone metrics on the state space of quantum systems, Quantum Inf. Comput., 6
2006
Later among the works it cites.
F. Liese and I. Vajda, On divergences and informations in statistics and information theory, IEEE Trans. Inform. Theory 52
2006
Later among the works it cites.
F. Hansen, Metric adjusted skew information, Proc. Natl. Acad. Sci. USA. 105
2008
Later among the works it cites.
D. Petz, Quantum Information Theory and Quantum Statistics
2008
Later among the works it cites.
P. Gibilisco, F. Hiai and D. Petz, Quantum covariance, quantum Fisher information and the uncertainty principle, IEEE Trans. Inform. Theory 55
2009
Later among the works it cites.
F. Hiai and D. Petz, Riemannian geometry on positive definite matrices related to means, Lin. Alg. Appl. 430
2009
Later among the works it cites.
D. Petz, From f f -divergence to quantum quasi-entropies and their use, Entropy 12
2010
Closest in time.
D. Petz and C. Ghinea, Introduction to quantum Fisher information, arXiv:1008.2417, 2010
Original
2010
Closest in time.

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