Year: 2026
Type: preprint
Abstract: In this paper, we study the properties of Connes spectral distances between quantum states under unitary transformations. We mainly focus on spectral triples with matrix algebras acting on finite dimensional Hilbert spaces. We prove that there are some finite spectral triples in which the Lipschitz seminorms are equal to the operator norms. We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quantum trace distances. These results are helpful for us to better study the relationships among Connes spectral distance, quantum trace distance and other quantum distance measures. These concrete examples are significant for studies of geometric structures of finite spectral triples and mathematical relations of qubits and other quantum states in the framework of noncommutative geometry.
Source: arXiv (Cornell University)
Authors: Lin, Bing-Sheng, Wang, Ji-Hong, You, Zhi-Kang
Institution: South China University of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G671680513
OpenAlex ID: W7161158094