Sharp estimates of quantum covering problems via a novel trace inequality

Hao-Chung Cheng; Li Gao; Christoph Hirche; Hao-Wei Huang; Po-Chieh Liu

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arXiv · 2507.07961

Sharp estimates of quantum covering problems via a novel trace inequality

Hao-Chung Cheng·Li Gao·Christoph Hirche·Hao-Wei Huang·Po-Chieh Liu

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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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BibTeX RIS

Hao-Chung Cheng, Li Gao, Christoph Hirche, Hao-Wei Huang, Po-Chieh Liu. 2025-07-10. Sharp estimates of quantum covering problems via a novel trace inequality. https://arxiv.org/abs/2507.07961

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