On the Joint Convexity of the Bregman Divergence of Matrices

@article{Pitrik2015OnTJ,
  title={On the Joint Convexity of the Bregman Divergence of Matrices},
  author={J. Pitrik and D'aniel Virosztek},
  journal={Letters in Mathematical Physics},
  year={2015},
  volume={105},
  pages={675-692}
}
We characterize the functions for which the corresponding Bregman divergence is jointly convex on matrices. As an application of this characterization, we derive a sharp inequality for the quantum Tsallis entropy of a tripartite state, which can be considered as a generalization of the strong subadditivity of the von Neumann entropy. (In general, the strong subadditivity of the Tsallis entropy fails for quantum states, but it holds for classical states.) Furthermore, we show that the joint… Expand
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