量子瓦瑟尔斯坦距离的量子比特状态空间等位性

arXiv - MATH - Metric Geometry Pub Date : 2024-08-19 DOI:arxiv-2408.09879

Richárd Simon, Dániel Virosztek

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引用次数: 0

摘要

本文研究量子比特态空间上量子瓦瑟斯坦距离和发散的等距。我们描述了关于对称量子瓦瑟斯坦发散 $d_{sym}$（由所有保利矩阵引起的发散）的等距。我们还给出了关于 $D_z$ 的等距的完整描述，即与单个保利矩阵 $\sigma_z$ 相对应的量子瓦瑟斯坦距离。

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Isometries of the qubit state space with respect to quantum Wasserstein distances

In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wasserstein divergence $d_{sym}$, the divergence induced by all of the Pauli matrices. We also give a complete characterization of isometries with respect to $D_z$, the quantum Wasserstein distance corresponding to the single Pauli matrix $\sigma_z$.

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arXiv - MATH - Metric Geometry

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