Based on the theory developed 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] leading to a Sinkhorn-like algorithm for Quantum optimal transport with convex regularisation, a block gradient ascent approach to Entropically Regularised Quantum Optimal Transport is discussed. A proof of a linear convergence rate based on strong concavity of the dual functional and some results of first numerical experiments will be discussed, cf. arXiv:2503.17590 (joint work with Max von Renesse).
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