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This paper establishes a fundamental mathematical result identifying the isometry group of $n$-qubit state spaces under quantum Wasserstein distance as precisely the Wigner symmetries. The finding bridges optimal transport theory with core principles of quantum mechanics, offering new theoretical tools for analyzing geometric structures in high-dimensional quantum systems. Such structural insights are critical for advancing foundational research into quantum information geometry and simulation algorithms.
Quantum Wasserstein isometries of the $n$-qubit state space: a Wigner-type result
arXiv:2602.08628v2 Announce Type: replace-cross 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.
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.
Mathematical Physics (math-ph); Operator Algebras (math.OA); Quantum Physics (quant-ph)
arXiv:2602.08628 [math-ph]
(or arXiv:2602.08628v2 [math-ph] for this version)
https://doi.org/10.48550/arXiv.2602.08628 Focus to learn more arXiv-issued DOI via DataCite
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