DOI QR코드

DOI QR Code

THE MATRIX GEOMETRIC MEANS UNDER PARTIAL TRACE

  • Kim, Sejong (Department of Mathematics Chungbuk National University)
  • Received : 2016.08.26
  • Accepted : 2016.12.16
  • Published : 2017.02.15

Abstract

We review a partial trace alternatively defined by the composition of positive linear maps, and see how the partial trace acts on the matrix geometric means. We also study the quantum Tsallis relative entropy under partial trace related with the fidelity.

Keywords

References

  1. S. Abe, Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification, Phys. Rev. A. 68 (2003), 032302. https://doi.org/10.1103/PhysRevA.68.032302
  2. R. Bhatia, Positive Definite Matrices, Princeton Series in Applied Mathematics, Princeton, NJ, 2007.
  3. S. Furuichi, K. Yanagi, and K. Kuriyama, Fundamental properties of Tsallis relative entropy, J. Math. Phys. 45 (2004), 4868-4877. https://doi.org/10.1063/1.1805729
  4. S. Kim, Operator entropy and fidelity associated with the geometric mean, Linear Algebra Appl. 438 (2013), 2475-2483. https://doi.org/10.1016/j.laa.2012.10.042
  5. J. Lawson and Y. Lim, Metric convexity of symmetric cones, Osaka J. Math., 44 (2007), 795-816.
  6. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010.
  7. K. Yanagi, K. Kuriyama, and S. Furuichi, Generalized Shannon inequalities based on Tsallis relative operator entropy, Linear Algebra Appl. 394 (2005), 109-118. https://doi.org/10.1016/j.laa.2004.06.025