Quantum Optimal Transport with Quantum Channels

@article{DePalma2019QuantumOT,
  title={Quantum Optimal Transport with Quantum Channels},
  author={Giacomo De Palma and Dario Trevisan},
  journal={Annales Henri Poincar{\'e}},
  year={2019},
  volume={22},
  pages={3199 - 3234}
}
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost. Our proposal is the first where the transport plans between quantum states are in natural correspondence with quantum channels, such that the transport can be interpreted as a physical operation on the system. Our main result is the proof of a modified triangle inequality for our transport distance. We… 

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