Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits

• URL: http://arxiv.org/abs/2510.26326v1
• Date: Thu, 30 Oct 2025 10:23:50 GMT
• Title: Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
• Authors: Gergely Bunth, József Pitrik, Tamás Titkos, Dániel Virosztek,
• Abstract summary: We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport.<n>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.
• Score: 1.3999481573773072
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, we use this information on optimal solutions to give an analytical proof of the triangle inequality for the induced quantum Wasserstein divergences.

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