Von Neumann Entropy by Logarithmic Method

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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