发表机构
Universität zu Köln; University of Camerino; Istituto Nazionale di Fisica Nucleare, Sezione di Perugia; Universitat Autònoma de Barcelona（科隆大学; 卡梅里诺大学; 意大利国家核物理研究所佩鲁吉亚分部; 巴塞罗那自治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过构造反例，证明量子信道的Holevo重心在信道与自身张量积下不具乘性，且其熵既非普遍次可加也非普遍超可加，否定了乘性普遍成立的猜想。
AI 中文摘要
量子信道的 Holevo 重心是唯一的输出态，它由任何达到 Holevo 容量的系综的平均输出获得。给定两个量子信道，乘性问题询问该重心在并行组合下是否张量化，即乘积信道的重心是否与各个重心的张量积一致。此问题与 Holevo 容量的可加性问题密切相关：可加性蕴含 Holevo 重心的张量化，而仅张量化不足以推出可加性。尽管已知有构造展示了存在具有非可加 Holevo 容量的信道，但其相应的 Holevo 重心仍然张量化，因此乘性是否最终普遍成立仍悬而未决。在此，我们通过展示信道与自身张量积下 Holevo 重心不具乘性的例子，对此问题给出否定回答。此外，我们证明 Holevo 重心的熵在张量积下既非普遍次可加，也非普遍超可加。
英文摘要
The Holevo barycenter of a quantum channel is the unique output state obtained as the average output of any ensemble achieving the Holevo capacity. Given two quantum channels, the multiplicativity problem asks whether this barycenter tensorizes under parallel composition, namely whether the barycenter of the product channel coincides with the tensor product of the individual barycenters. This question is closely related to the additivity problem for the Holevo capacity: additivity implies tensorization of the Holevo barycenter, while tensorization alone is not sufficient for additivity. Although a construction is known that demonstrates the existence of channels with non-additive Holevo capacity, their corresponding Holevo barycenters still tensorize, leaving open whether multiplicativity might ultimately hold universally. Here, we answer this question in the negative by exhibiting channels for which the Holevo barycenter is not multiplicative under the tensor product of the channel with itself. Moreover, we show that the entropy of the Holevo barycenter is neither universally subadditive nor universally superadditive under tensor product.
