Basic Entropies for Positive-Definite Matrices
Basic Entropies for Positive-Definite Matrices
摘要
We extend basic entropies in the classical information theory to matrix ones in the quantum information theory. Then we show that relations between matrix entropies similar to the classical ones hold.
参考文献19
-
1E. Andruchow, G. Corach and D. Stojanoff: Geometrical significance of Lowner-Heinz inequality, Proc. Amer. Math. Soc., 128 (2000), 1031-1037.
-
2V.P. Belavkin, P. Staszewski: C*-algebraic generalization of relative entropy and entropy, Ann. Inst. H. Poincare Sect. A.37(1982), 51-58.
-
3G. Corach, H. Porta and L. Recht: Geodesics and operator means in the space of positive operators, lnternat. J. Math. 4 (1993), 193-202.
-
4G. Corach and A.L.Maestripieri: Differential and metrical structure of positive operators, Positivity 3 (1999), 297-315.
-
5R.G. Douglas: On majorization, factorization and range inclusion of operators in Hilbert space, Proc. Amer. Math. Sot., 17 (1966), 413-416.
-
6J. 1. Fujii: The Hiai-Petz geodesic for strongly convex norm is the unique shortest path, Sci. Math. Japon. Online, e-2009 (2009), 579-586.
-
7J. I. Fujii: Structure of Hiai-Petz parametrized geometry for positive definite matrices, Linear Algebra. Appl. 432 (2010), 318-326.
-
8J. I. Fujii, M. Fujii and Y. Seo: An extension of the Kubo -Ando theory : Solidarities, Math. Japon., 35 (1990), 509-512.
-
9J. I. Fujii and E. Kamei: Relative operator entropy in noncommutative information theory, Math. Japon. 34 (1989), 341-348.
-
10J.I.Fujii and E.Kamei: Uhlmann's interpolational method for operator means, Math. Japon. 34 (1989), 541--547.
-
1代雄平,周作领,耿祥义.Some relations between Hausdorff-dimensions and entropies[J].Science China Mathematics,1998,41(10):1068-1075.
-
2Hiroshi Isa,Masatoshi Ito,Eizaburo Kamei,Hiroaki Tohyama,MasayukiWatanabe.Expanded Relative Operator Entropies and Operator Valued α-Divergence[J].Journal of Mathematics and System Science,2015,5(6):215-224.
-
3Alexey E.Rastegin.Uncertainty and Certainty Relations for Pauli Observables in Terms of R′enyi Entropies of Order α ∈(0;1][J].Communications in Theoretical Physics,2014,61(3):293-298. 被引量:1
-
4CAO Ye,LI Hui,LONG GuiLu.Entanglement of linear cluster states in terms of averaged entropies[J].Chinese Science Bulletin,2013,58(1):48-52. 被引量:6
-
5Alexey E. Rastegin.Generalized Conditional Entropies of Partitions on Quantum Logic[J].Communications in Theoretical Physics,2012,58(12):819-822. 被引量:1
-
6Alexey E.Rastegin.Uncertainty and Certainty Relations for Successive Projective Measurements of a Qubit in Terms of Tsallis' Entropies[J].Communications in Theoretical Physics,2015,63(6):687-694.
-
7陈贵强,陆云光.CONVERGENCE OF THE APPROXIMATE SOLUTIONS TO ISENTROPIC GAS DYNAMICS[J].Acta Mathematica Scientia,1990,10(1):39-45.
-
8陆善镇.ON EXISTENCE OF ENTROPY OF CONJUGATE FUNCTIONS[J].Chinese Science Bulletin,1984,29(6):722-726.
-
9CHENGUIQIANG,P.G.LEFLOCH.ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS[J].Chinese Annals of Mathematics,Series B,2001,22(2):145-158.
-
10Sun Guo-Hua,Duan Popov,Oscar Camacho-Nieto,Dong Shi-Hai.Shannon information entropies for position-dependent mass Schrdinger problem with a hyperbolic well[J].Chinese Physics B,2015,24(10):45-52.