Discrete mathematics

Quantum entanglement

Physics

Quantum discord

Kullback–Leibler divergence

Quantum relative entropy

Mathematics

Logarithm

Principle of maximum entropy

Semidefinite programming

Entropy (arrow of time)

Conditional entropy

Statistical physics

Statistics

Mathematical optimization

Quantum state

Counterexample

Mathematical analysis

Quantum information

Joint quantum entropy

Separable state

Quantum mechanics

Generalized relative entropy

Quantum

Journal of Physics A Mathematical and Theoretical

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.

Efficient optimization of the quantum relative entropy