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Quantum Wasserstein isometries of the $n$-qubit state space: a Wigner-type result
Gergely Bunth, Eszter Szabó, Dániel Virosztek·February 9, 2026
Mathematical Physicsmath.OAQuantum Physics
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Abstract
We determine the isometry group of the $n$-qubit state space with respect to the quantum Wasserstein distance induced by the so-called symmetric transport cost for all $n \in \mathbb{N}.$ It turns out that the isometries are precisely the Wigner symmetries, that is, the unitary or anti-unitary conjugations.