Metric-adjusted skew information: Convexity and restricted forms of superadditivity

Letters in Mathematical Physics

Volumn 93, Issue 1, 2010, Pages 1-13

  Cai, Liang ^a   Hansen, Frank ^b  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Metric adjusted skew information; Monotone metric; Superadditivity; Wigner Yanase Dyson skew information

Indexed keywords

EID: 77952310431     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-010-0396-2     Document Type: Article

References (29)

1. Andai A.: Uncertainty principle with quantum Fisher information. J. Math. Phys. 49, 012106 (2008).
2. Araki H., Yanase M. M.: Measurement of quantum mechanical operators. Phys. Rev. 120, 622-626 (1960).
3. Audenaert K., Cai L., Hansen F.: Inequalities for quantum skew information. Lett. Math. Phys. 85, 135-146 (2008).
4. Bendat J., Sherman S.: Monotone and convex operator functions. Trans. Am. Math. Soc. 79, 58-71 (1955).
5. Cai L., Li N., Luo S.: Weak superadditivity of skew information. J. Phys. A: Math. Theor. 41, 135301 (2008).
6. Censov, N. N.: Statistical decision rules and optimal inferences. Translation of Mathematical Monographs, vol. 53. American Mathematical Society, Providence (1982).
7. Effros E. G.: A matrix convexity approach to some celebrated quantum inequalities. Proc. Natl. Acad. Sci. USA 106, 1006-1008 (2009).
8. Gibilisco P., Hansen F., Isola T.: On a correspondence between regular and non-regular operator monotone functions. Linear Algebra Appl. 430, 2225-2232 (2009).
9. Gibilisco P., Imparato D., Isola T.: Uncertainty principle and quantum Fisher information II. J. Math. Phys. 48, 072109 (2007).
10. Hansen F.: Extensions of Lieb's concavity theorem. J. Stat. Phys. 124, 87-101 (2006).
11. Hansen F.: The Wigner-Yanase entropy is not subadditive. J. Stat. Phys. 126, 643-648 (2007).
12. Hansen F.: Metric adjusted skew information. Proc. Natl. Acad. Sci. USA 105, 9909-9916 (2008).
13. Hansen F., Pedersen G. K.: Jensen's inequality for operators and Löwner's theorem. Math. Ann. 258, 229-241 (1982).
14. Hasegawa H.: α-divergence of the non-commutative information geometry. Rep. Math. Phys. 33, 87-93 (1993).
15. Hasegawa H., Petz D.: On the Riemannian metric of α-entropies of density matrices. Lett. Math. Phys. 38, 221-225 (1996).
16. Hasegawa H., Petz D.: Non-commutative extension of the information geometry II. In: Hirota, O. (eds) Quantum Communication and Measurement, pp. 109-118. Plenum, New York (1997).
17. Jencǒvá, A., Ruskai, M. B.: A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality. ArXiv: 0903. 2895 v3.
18. Lesniewski A., Ruskai M. B.: Monotone Riemannian metrics and relative entropy on non-commutative probability spaces. J. Math. Phys. 40, 5702-5724 (1999).
19. Lieb E. H.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 11, 267-288 (1973).
20. Luo S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403 (2003).
21. Luo S.: Wigner-Yanase skew information vs. quantum Fisher information. Proc. Am. Math. Soc. 132, 885-890 (2003).
22. Luo S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008).
23. Luo S.: Notes on superadditivity of Wigner-Yanase-Dyson information. J. Stat. Phys. 128, 1177-1188 (2007).
24. Luo S., Zhang Q.: Superadditivity of Wigner-Yanase-Dyson information revisited. J. Stat. Phys. 131, 1169-1177 (2008).
25. Morozova, E. A., Chentsov, N. N.: Markov invariant geometry on state manifolds (Russian). Itogi Nauki i Techniki, 36, 69-102 (1990). Translated in J. Sov. Math. Soc. 56, 2648-2669 (1991).
26. Petz D.: Quasi-entropies for finite quantum systems. Rep. Math. Phys. 23, 57-65 (1986).
27. Petz D.: Monotone metrics on matrix spaces. Linear Algebra Appl. 244, 81-96 (1996).
28. Wigner E. P.: Die Messung quantenmechanischer Operatoren. Z. Physik 133, 101-108 (1952).
29. Wigner E. P., Yanase M. M.: Information contents of distributions. Proc. Natl. Acad. Sci. USA 49, 910-918 (1963).