Sharp estimates of quantum covering problems via a novel trace inequality
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909682994511872 |
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| author | Cheng, Hao-Chung Gao, Li Hirche, Christoph Huang, Hao-Wei Liu, Po-Chieh |
| author_facet | Cheng, Hao-Chung Gao, Li Hirche, Christoph Huang, Hao-Wei Liu, Po-Chieh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07961 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp estimates of quantum covering problems via a novel trace inequality Cheng, Hao-Chung Gao, Li Hirche, Christoph Huang, Hao-Wei Liu, Po-Chieh Quantum Physics Information Theory Functional Analysis Operator Algebras 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. |
| title | Sharp estimates of quantum covering problems via a novel trace inequality |
| topic | Quantum Physics Information Theory Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2507.07961 |