Monotonicity of a relative Rényi entropy

Journal of Mathematical Physics

Volumn 54, Issue 12, 2013, Pages

  Frank, Rupert L ^a   Lieb, Elliott H ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84891535488     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4838835     Document Type: Article

References (15)

1. Ando T. Convexity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra Appl. 1979, 26:203-241. 10.1016/0024-3795(79)90179-4
2. Bekjan T. On joint convexity of trace functions. Linear Algebra Appl. 2004, 390:321-327. 10.1016/j.laa.2004.05.002
3. Beigi S. Sandwiched Rényi divergence satisfies data processing inequality. J. Math. Phys. 2013, 54:122202. 10.1063/1.4838855, e-print arXiv:1306.5920.
4. Carlen E.A. Trace inequalities and quantum entropy. An introductory course. Entropy and the Quantum 2010, 529:73-140. in Contemporary Mathematics Vol. (American Mathematical Society, Providence, RI)
5. Carlen E.A. Lieb E.H. A Minkowski type trace inequality and strong subadditivity of quantum entropy II: convexity and concavity. Lett. Math. Phys. 2008, 83:107-126. 10.1007/s11005-008-0223-1
6. Epstein H. Remarks on two theorems of E. Lieb. Commun. Math. Phys. 1973, 31:317-325. 10.1007/BF01646492
7. Jaksic V. Ogata Y. Pautrat Y. Pillet C.-A. Entropic fluctuations in quantum statistical mechanics. An introduction. Quantum Theory from Small to Large Scales 2012, 95. in Lecture Notes of the Les Houches Summer School Vol. (Oxford University Press).
8. Lieb E.H. Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 1973, 11:267-288. 10.1016/0001-8708(73)90011-X
9. Lieb E.H. Thirring W. Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. Studies in Mathematical Physics: Essays in Honor of Valentine Bargman 1976, 269-297. E. H. Lieb, B. Simon, A. S. Wightman, in edited by and (Princeton University Press, Princeton)
10. Lindblad G. Expectations and entropy inequalities for finite quantum systems. Commun. Math. Phys. 1974, 39:111-119. 10.1007/BF01608390
11. Mosonyi M. Hiai F. On the quantum Rényi relative entropies and related capacity formulas. IEEE Trans. Inf. Theory 2011, 57(4):2474-2487. 10.1109/TIT.2011.2110050
12. Müller-Lennert M. On quantum Rényi entropies: new definition, some properties. J. Math. Phys. 2013, 54:122203. 10.1063/1.4838856, e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142.
13. Stinespring W.F. Positive functions on C*-algebras. Proc. Am. Math. Soc. 1955, 6:211-216. 10.1090/S0002-9939-1955-0069403-4
14. Uhlmann A. Endlich-dimensionale Dichtematrizen II. Wiss. Z. Karl-Marx-Univ. Leipzig, Math.-Nat. R. 1973, 22:139-177.
15. Wilde M.M. Winter A. Yang D. Strong converse for the classical capacity of entanglement-breaking channels. e-print arXiv:1306.1586.