Quantum Wasserstein isometries with a single observable generating the transport cost

We consider quantum Wasserstein distances where the transport cost is generated by a single observable quantity, and study the isometries of quantum state spaces with respect to these distances. The main result is an extension of Theorem 2 in [R. Simon, D. Virosztek, Linear Algebra Appl. 714 (2025), 1–14], which describes the qubit Wasserstein isometries induced by a single observable, to finite quantum systems of arbitrary dimensions.