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

Bunth, Gergely, Pitrik, József, Titkos, Tamás ORCID: https://orcid.org/0000-0002-3891-7020 and Virosztek, Dániel ORCID: https://orcid.org/0000-0003-1109-5511 (2026) Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits. Linear algebra and its applications . DOI 10.1016/j.laa.2026.04.028

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Official URL: https://doi.org/10.1016/j.laa.2026.04.028

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. © 2026 The Author(s)

Item Type:

Article

Uncontrolled Keywords:

Optimal solutions; Optimal systems; Quantum chemistry; Costs; quantum communication; Quantum electronics; Quantum channel; Communication channels (information theory); Transport problems; Triangle inequality; Dual problem; quantum channels; Optimal transport; Quantum optimal transport; Generic cost;

Divisions:

Institute of Data Analytics and Information Systems

Subjects:

Mathematics, Econometrics

Funders:

Momentum Program of the Hungarian Academy of Sciences, Hungarian National Research, Development and Innovation Office, ERC Synergy

Projects:

LP2021-15/2021, KKP133827, K134944 and no. Excellence_151232, 810115

DOI:

10.1016/j.laa.2026.04.028

ID Code:

12848