1304.7442 (Yuan Li et al.)

Von Neumann entropy and majorization    [PDF]

Yuan Li, Paul Busch

In this paper, we firstly consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalized Uhlmann theorem in an infinite dimension Hilbert space. Also, we show that $S(\Phi(\rho))=S(\rho)$ for all quantum states $\rho$ if and only if there exists an isometry operator $V$ such that $\Phi(\rho)=V\rho V^*,$ where $\Phi$ is a quantum channel.

View original: http://arxiv.org/abs/1304.7442