Sharp estimates of quantum covering problems via a novel trace inequality

• URL: http://arxiv.org/abs/2507.07961v1
• Date: Thu, 10 Jul 2025 17:41:50 GMT
• Title: Sharp estimates of quantum covering problems via a novel trace inequality
• Authors: Hao-Chung Cheng, Li Gao, Christoph Hirche, Hao-Wei Huang, Po-Chieh Liu,
• Abstract summary: We prove a novel trace inequality involving two operators.<n>We sharpen the one-shot achievability bound on the relative entropy error in a wealth of quantum covering-type problems.
• Score: 14.63459736743123
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we prove a novel trace inequality involving two operators. As applications, we sharpen the one-shot achievability bound on the relative entropy error in a wealth of quantum covering-type problems, such as soft covering, privacy amplification, convex splitting, quantum information decoupling, and quantum channel simulation by removing some dimension-dependent factors. Moreover, the established one-shot bounds extend to infinite-dimensional separable Hilbert spaces as well. The proof techniques are based on the recently developed operator layer cake theorem and an operator change-of-variable argument, which are of independent interest.

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