Continuity bounds on the quantum relative entropy -- II

@article{Audenaert2005ContinuityBO,
  title={Continuity bounds on the quantum relative entropy -- II},
  author={Koenraad M. R. Audenaert and Jens Eisert},
  journal={Journal of Mathematical Physics},
  year={2005},
  volume={46},
  pages={102104}
}
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have derived many such inequalities in previous work. The present paper is a follow-up on this, and provides a sharp upper bound on the relative entropy in terms of the trace norm distance and of the smallest eigenvalues of both states concerned. The result… 
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