Hilbert's projective metric in quantum information theory

@article{Reeb2011HilbertsPM,
  title={Hilbert's projective metric in quantum information theory},
  author={David Reeb and Michael J. Kastoryano and Michael M. Wolf},
  journal={Journal of Mathematical Physics},
  year={2011},
  volume={52},
  pages={082201}
}
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or positive partial transpose operators. It provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under protocols involving local quantum operations and classical communication or under other cone-preserving operations. The results are formulated in terms of… 
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