On average output entropy of a quantum channel
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911836483354624 |
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| author | Shirokov, M. E. |
| author_facet | Shirokov, M. E. |
| contents | We describe analytical properties of the average output entropy of a quantum channel as a function of a pair (channel, input ensemble). In particular, tight semicontinuity bounds for this function with the rank/energy constraints are obtained by using the modified semicontinuity bounds for the quantum conditional entropy of quantum-classical states and a special approximation technique.
Several applications are considered. New semicontinuity and continuity bounds for the output Holevo information of a channel as a function of a pair (channel, input ensemble) are obtained. The semicontinuity bound for the entanglement of formation with the rank constraint obtained in [1] is improved.
In the preliminary part, some results concerning ensembles of quantum states are presented. In particular, a new useful metric on the set of generalized ensembles is proposed and explored. The concept of passive energy of an ensemble introduced here plays an important role in the article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On average output entropy of a quantum channel Shirokov, M. E. Quantum Physics Mathematical Physics We describe analytical properties of the average output entropy of a quantum channel as a function of a pair (channel, input ensemble). In particular, tight semicontinuity bounds for this function with the rank/energy constraints are obtained by using the modified semicontinuity bounds for the quantum conditional entropy of quantum-classical states and a special approximation technique. Several applications are considered. New semicontinuity and continuity bounds for the output Holevo information of a channel as a function of a pair (channel, input ensemble) are obtained. The semicontinuity bound for the entanglement of formation with the rank constraint obtained in [1] is improved. In the preliminary part, some results concerning ensembles of quantum states are presented. In particular, a new useful metric on the set of generalized ensembles is proposed and explored. The concept of passive energy of an ensemble introduced here plays an important role in the article. |
| title | On average output entropy of a quantum channel |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2404.07978 |