Recognition: unknown
Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
read the original abstract
We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport. As an application, we determine optimal solutions of both the primal and the dual problem using this duality in the case of quantum bits and distinguished cost operators, with certain restrictions on the states involved. Finally, keeping the same restrictions regarding the states involved, we use this information on optimal solutions to give an analytical proof of the triangle inequality even for the square of the induced quantum Wasserstein divergences.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Relations between different definitions of the quantum Wasserstein distance for qubits
Two quantum Wasserstein distance definitions coincide for qubits with single-operator cost functions, implying the self-distance equals the Wigner-Yanase skew information.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.