基于 telescoping 的量子态全平滑单射多户覆盖与解耦
量子物理
2025-04-10 v2
摘要
我们证明了全平滑单射多户覆盖（即凸分割）结果以及量子态全平滑多户解耦结果。此前文献中尚未知晓全平滑单射结果：Cheng、Gao和Berta（arXiv:2304.12056）关于凸分割，以及Colomer和Winter（arXiv:2304.12114）关于解耦，已通过引入一种称为“telescoping cum mean zero分解”的技术取得了实质性进展。我们展示，telescoping cum mean zero分解技术实际上可以被简化并进一步扩展，以证明全平滑解耦和凸分割结果。我们的技术手段允许我们首次为各种基本网络量子信息论问题证明首个全平滑单射内界，例如Anshu、Jain和Warsi（arXiv:1703.09961）提出的广义Slepian Wolf问题。我们还首次证明了Chakraborty、Nema和Sen（arXiv::2102.02187）首次猜想的量子多访问信道在有限纠缠帮助下的自然多面体内界。
关键词
引用
@article{arxiv.2410.17893,
title = {Fully smooth one shot multipartite covering and decoupling of quantum states via telescoping},
author = {Pranab Sen},
journal= {arXiv preprint arXiv:2410.17893},
year = {2025}
}
备注
37 pages. The results on multipartite soft covering in concentration as well as its application to a wiretap channel with many non-interacting eavesdroppers found in v1 have been moved to a new paper (arXiv:2504.04067). That paper also contains a new expander matrix Chernoff bound