On Strong Converse Bounds for the Private and Quantum Capacities of Anti-degradable Channels
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912494804533248 |
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| author | Khanian, Zahra Baghali Hirche, Christoph |
| author_facet | Khanian, Zahra Baghali Hirche, Christoph |
| contents | We establish a strong converse bound for the private classical capacity of anti-degradable quantum channels. Specifically, we prove that this capacity is zero whenever the error $ε> 0$ and privacy parameter $δ> 0$ satisfy the inequality $δ(1-ε^2)^{\frac{1}{2}}+ε(1-δ^2)^{\frac{1}{2}}<1$. This result strengthens previous understandings by sharply defining the boundary beyond which reliable and private communication is impossible. Furthermore, we present a ``pretty simple'' proof of the ``pretty strong'' converse for the quantum capacity of anti-degradable channels, valid for any error $ε< \frac{1}{\sqrt{2}}$. Our approach offers clarity and technical simplicity, shedding new light on the fundamental limits of quantum communication. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_15661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Strong Converse Bounds for the Private and Quantum Capacities of Anti-degradable Channels Khanian, Zahra Baghali Hirche, Christoph Quantum Physics Information Theory We establish a strong converse bound for the private classical capacity of anti-degradable quantum channels. Specifically, we prove that this capacity is zero whenever the error $ε> 0$ and privacy parameter $δ> 0$ satisfy the inequality $δ(1-ε^2)^{\frac{1}{2}}+ε(1-δ^2)^{\frac{1}{2}}<1$. This result strengthens previous understandings by sharply defining the boundary beyond which reliable and private communication is impossible. Furthermore, we present a ``pretty simple'' proof of the ``pretty strong'' converse for the quantum capacity of anti-degradable channels, valid for any error $ε< \frac{1}{\sqrt{2}}$. Our approach offers clarity and technical simplicity, shedding new light on the fundamental limits of quantum communication. |
| title | On Strong Converse Bounds for the Private and Quantum Capacities of Anti-degradable Channels |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2507.15661 |