On a correspondence between regular and non-regular operator monotone functions

Linear Algebra and Its Applications

Volumn 430, Issue 8-9, 2009, Pages 2225-2232

  Gibilisco, P ^a   Hansen, F ^b   Isola, T ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Matrix means; Operator monotone functions; Quantum Fisher information

Indexed keywords

MATHEMATICAL OPERATORS;

BIJECTION; FUNCTIONAL EQUATIONS; MATRIX MEANS; MONOTONICITY; OPERATOR MONOTONE FUNCTIONS; QUANTUM FISHER INFORMATION; REGULAR OPERATORS; SKEW INFORMATIONS;

FISHER INFORMATION MATRIX;

EID: 61449215016     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.11.022     Document Type: Article

References (22)

1. Audenaert K., Cai L., and Hansen F. Inequalities for quantum skew information. Lett. Math. Phys. 85 (2008) 135-146
2. Calsamiglia J., Munoz-Tapia R., Masanes L., Acin A., and Bagan E. Quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states. Phys. Rev. A 77 (2008) 032311
3. Carlen E. Superadditivity of Fisher's information and logarithmic Sobolev inequalities. J. Funct. Anal. 101 1 (1991) 194-211
4. Chen Z. Wigner-Yanase skew information as tests for quantum entanglement. Phys. Rev. A 71 (2005) 052302
5. Čencov N.N. Statistical decision rules and optimal inference (1982), American Mathematical Society, Providence, R.I.
6. 1. J. Funct. Anal. 28 (1978) 187-196
7. E. Fick, G. Sauermann, The quantum statistics of dynamic processes, Springer Series in Solid-State Sciences, vol. 86, Berlin, 1990.
8. Gibilisco P., Imparato D., and Isola T. Uncertainty principle and quantum Fisher information II. J. Math. Phys. 48 (2007) 072109
9. Gibilisco P., and Isola T. A dynamical uncertainty principle in von Neumann algebras by operator monotone functions. J. Stat. Phys. 132 (2008) 937-944
10. Hansen F. Metric adjusted skew information. Proc. Natl. Acad. Sci. USA 105 (2008) 9909-9916
11. Hansen F., and Pedersen G.K. Jensen's operator inequality and Löwner's theorem. Math. Ann. 258 (1982) 229-241
12. Hasegawa H., and Petz D. On the Riemannian metric of α-entropies of density matrices. Lett. Math. Phys. 38 (1996) 221-225
13. Hasegawa H., and Petz D. Non-commutative extension of information geometry II. In: Hirota O., et al. (Ed). Quantum Communication, Computing and Measurement (1997), Plenum
14. Klyachko A., Oztop B., and Shumovsky A.S. Measurable entanglement. Appl. Phys. Lett. 88 (2006) 124102
15. Kubo F., and Ando T. Means of positive linear operators. Math. Ann. 246 3 (1979/1980) 205-224
16. Lieb E. Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 11 (1973) 267-288
17. Lieb E., and Ruskai M.B. A fundamental property of the quantum mechanical entropy. Phys. Rev. Lett. 30 (1973) 434436
18. Löwner K. Über monotone Matrixfunktionen. Math. Zeit. 38 (1934) 177-216
19. Petz D. Monotone metrics on matrix spaces. Linear Algebra Appl. 244 (1996) 81-96
20. Petz D., and Sudár C. Geometry of quantum states. J. Math. Phys. 37 (1996) 2662-2673
21. Szabó V.E.S. A class of matrix monotone functions. Linear Algebra Appl. 420 (2007) 79-85
22. Wigner E.P., and Yanase M.M. Information contents of distributions. Proc. Nat. Acad. Sci. USA 49 (1963) 910-918