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arXiv · 1705.06671

Efficient optimization of the quantum relative entropy

Hamza Fawzi·Omar Fawzi
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Abstract

Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable states. The various capacities of quantum channels can also be written in this way. We propose a unified framework to numerically compute these quantities using off-the-shelf semidefinite programming solvers, exploiting the approximation method proposed in [Fawzi, Saunderson, Parrilo, Semidefinite approximations of the matrix logarithm, arXiv:1705.00812]. As a notable application, this method allows us to provide numerical counterexamples for a proposed lower bound on the quantum conditional mutual information in terms of the relative entropy of recovery.

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Hamza Fawzi, Omar Fawzi. 2017-05-18. Efficient optimization of the quantum relative entropy. https://doi.org/10.1088/1751-8121%2Faab285

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