Dual Block Gradient Ascent for Entropically Regularised Quantum Optimal Transport

We present a block gradient ascent method for solving the quantum optimal transport problem with entropic regularisation similar to the algorithm proposed in [D. Feliciangeli, A. Gerolin, L. Portinale: J. Funct. Anal. 285 (2023), no. 4, 109963] and [E. Caputo, A. Gerolin, N. Monina, L. Portinale: arXiv:2409.03698]. We prove a linear convergence rate based on strong concavity of the dual functional and present some results of numerical experiments of an implementation.