近日，匈牙利阿尔弗雷德·雷尼数学所的Gergely Bunth及其研究团队取得一项新进展。经过不懈努力，他们揭示量子沃瑟斯坦散度的度量性质。相关研究成果已于2024年8月7日在国际知名学术期刊《物理评论A》上发表。

该研究团队证明了在特定状态为纯态且所有状态具有有限能量的情况下，对于由可分离希尔伯特空间描述的每个量子系统和任意二次成本算子，量子沃瑟斯坦散度满足三角不等式。研究人员还提供了强有力的数值证据，表明对于任意选择的状态，三角不等式通常都成立。

据悉，量子沃瑟斯坦散度是量子沃瑟斯坦距离通过通道定义的修正版本，德帕尔马和特雷维桑推测它们是量子态空间上的真正度量。

附：英文原文

Title: Metric property of quantum Wasserstein divergences

Author: Gergely Bunth, József Pitrik, Tamás Titkos, Dániel Virosztek

Issue&Volume: 2024/08/07

Abstract: Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels and they have been conjectured to be genuine metrics on quantum state spaces by De Palma and Trevisan. We prove triangle inequality for quantum Wasserstein divergences for every quantum system described by a separable Hilbert space and any quadratic cost operator under the assumption that a particular state involved is pure and all the states have finite energy. We also provide strong numerical evidence suggesting that the triangle inequality holds in general for an arbitrary choice of states.

DOI: 10.1103/PhysRevA.110.022211

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.022211