Von  Von Neumann Entropy by Logarithmic Method: Mathematics-Physics

Bijan Nikouravan

doi:10.14331/ijfps.2019.330132

Authors

Bijan Nikouravan Department of Physics, Islamic Azad University (IAU),Varamin-Pishva Branch, Iran

DOI:

https://doi.org/10.14331/ijfps.2019.330132

Keywords:

Entropy, Von Neumann entropy, linearity

Abstract

The Von Neumann entropy plays a central role in the quantum information theory and is a concave function and following the property . In this paper, we introduce a new proof for the linearity of Von Neumann entropy in the rate without using the above inequality. Here the Von Neumann entropy is concave; that is, given weights and density matrices . Roughly speaking, we will show that in the rate case, the Von Neumann entropy is linear without using Fannes inequality.

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Author Biography

Bijan Nikouravan, Department of Physics, Islamic Azad University (IAU),Varamin-Pishva Branch, Iran

Dr. Bijan Nikouravan

REFERNCES

Audenaert, K. M. (2007). A sharp continuity estimate for the von Neumann entropy. Journal of Physics A: Mathematical and Theoretical, 40(28), 8127.

Garbaczewski, P. (2005). Differential entropy and time. Entropy, 7(4), 253-299.

Jaeger, G. (2007). Quantum information: Springer.

Jaynes, E. T. (1965). Gibbs vs Boltzmann entropies. American Journal of Physics, 33(5), 391-398.

Kullback, S. (1968). Information Theory and Statistics. Courier Corporation. image analysis. Composites Science and Technology, 59(4), 543-545.

Neumann, J. v. (2013). Mathematische grundlagen der quantenmechanik (Vol. 38): Springer-Verlag.

Nielsen, M. A., & Chuang, I. L. (2000). Quantum information and quantum computation. Cambridge: Cambridge University Press, 2(8), 23.

Shannon, C. E. (1948). A mathematical theory of communication. Bell system technical journal, 27(3), 379-423.

Tomamichel, M., Colbeck, R., & Renner, R. (2010). Duality between smooth min-and max-entropies. IEEE Transactions on information theory, 56(9), 4674-4681.

von NEUMANN, J., & BEYER, R. T. (1955). Mathematische Grundlagen der Quantenmechanik. Mathematical Foundations of Quantum Mechanics... Translated... by Robert T. Beyer: Princeton University Press.