Bargmann invariants and local unitary equivalence

Abstract:In this paper, we study the local unitary equivalence of quantum states on $\mathbb{C}^n\otimes\mathbb{C}^n$, which is an important notion in quantum information theory. For the case $n=2$, the local unitary orbits of two-qubit states are completely determined by their local unitary Bargmann invariants. We show that the local unitary Bargmann invariants do not form a complete set of invariants of local unitary orbits for $n\geqslant 3$, which negatively answers a problem proposed by L. Zhang and B. Xie.

Quantum Physics (quant-ph); Operator Algebras (math.OA)

arXiv:2607.16878 [quant-ph]

(or arXiv:2607.16878v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.16878 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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