Three-Receiver Quantum Broadcast Channels: Classical Communication with Quantum Non-unique Decoding
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910487297392640 |
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| author | Salek, Farzin Hayden, Patrick Hayashi, Masahito |
| author_facet | Salek, Farzin Hayden, Patrick Hayashi, Masahito |
| contents | In network communication, it is common in broadcasting scenarios for there to exist a hierarchy among receivers based on information they decode due, for example, to different physical conditions or premium subscriptions. This hierarchy may result in varied information quality, such as higher-quality video for certain receivers. This is modeled mathematically as a degraded message set, indicating a hierarchy between messages to be decoded by different receivers, where the default quality corresponds to a common message intended for all receivers, a higher quality is represented by a message for a smaller subset of receivers, and so forth. We extend these considerations to quantum communication, exploring three-receiver quantum broadcast channels with two- and three-degraded message sets. Our technical tool involves employing quantum non-unique decoding, a technique we develop by utilizing the simultaneous pinching method. We construct one-shot codes for various scenarios and find achievable rate regions relying on various quantum Rényi mutual information error exponents. Our investigation includes a comprehensive study of pinching across tensor product spaces, presenting our findings as the asymptotic counterpart to our one-shot codes. By employing the non-unique decoding, we also establish a simpler proof to Marton's inner bound for two-receiver quantum broadcast channels without the need for more involved techniques. Additionally, we derive no-go results and demonstrate their tightness in special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-Receiver Quantum Broadcast Channels: Classical Communication with Quantum Non-unique Decoding Salek, Farzin Hayden, Patrick Hayashi, Masahito Quantum Physics Information Theory In network communication, it is common in broadcasting scenarios for there to exist a hierarchy among receivers based on information they decode due, for example, to different physical conditions or premium subscriptions. This hierarchy may result in varied information quality, such as higher-quality video for certain receivers. This is modeled mathematically as a degraded message set, indicating a hierarchy between messages to be decoded by different receivers, where the default quality corresponds to a common message intended for all receivers, a higher quality is represented by a message for a smaller subset of receivers, and so forth. We extend these considerations to quantum communication, exploring three-receiver quantum broadcast channels with two- and three-degraded message sets. Our technical tool involves employing quantum non-unique decoding, a technique we develop by utilizing the simultaneous pinching method. We construct one-shot codes for various scenarios and find achievable rate regions relying on various quantum Rényi mutual information error exponents. Our investigation includes a comprehensive study of pinching across tensor product spaces, presenting our findings as the asymptotic counterpart to our one-shot codes. By employing the non-unique decoding, we also establish a simpler proof to Marton's inner bound for two-receiver quantum broadcast channels without the need for more involved techniques. Additionally, we derive no-go results and demonstrate their tightness in special cases. |
| title | Three-Receiver Quantum Broadcast Channels: Classical Communication with Quantum Non-unique Decoding |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2406.09854 |