AI 中文总结
该研究针对量子信道识别任务，证明纠缠辅助传输容量是其强逆界，低噪声信道中二者相等，一般信道中存在严格不等的转置退极化信道，还得到识别容量严格超加性的首个实例。
AI 中文摘要
通过噪声信道进行经典识别是一项通信任务，其中接收方无需重构完整的传输消息，仅需判定该消息是否与某一感兴趣的消息一致。这种放松要求使得可识别消息的数量能随块长呈双指数增长。对于量子信道，由此产生的（双指数）识别容量$C_{\text{ID}}$可严格超过普通（指数）传输容量$C$。本文证明，纠缠辅助传输容量$C_E$是该任务的强逆界：$C_{\text{ID}} \leq C_E$。对于足够低噪声的信道，该界也可通过Hayden-Winter（量子）识别+指纹编码实现，这为这类信道的识别容量给出了精确刻画$C_{\text{ID}}=C_E$。然而，对于一般信道，本文证明该上界可以是严格的。本文给出了一类明确的转置退极化信道，其中$C_{\text{ID}}<C_E$。由此，本文还得到了识别容量$C_{\text{ID}}$严格超加性的首个实例。
英文摘要
Classical identification via a noisy channel is a communication task in which the receiver is not required to reconstruct the full transmitted message, but only to decide whether it coincides with a message of interest. This relaxation allows the number of identifiable messages to grow doubly exponentially with the blocklength. For quantum channels, the resulting (doubly exponential) identification capacity $C_{\mathrm{ID}}$ can strictly exceed the ordinary (exponential) transmission capacity $C$. In this paper, we prove that the entanglement-assisted transmission capacity $C_E$ is a strong converse bound for this task: $C_{\mathrm{ID}}\leq C_E$. For sufficiently low-noise channels, this bound can also be achieved via the Hayden-Winter (quantum) identification + fingerprinting codes. This yields an exact characterization $C_{\mathrm{ID}}=C_E$ of identification capacity for such channels. However, for general channels, we prove that this upper bound can be strict. We exhibit an explicit family of transpose-depolarizing channels for which $C_{\mathrm{ID}}<C_E$. As a consequence, we also obtain the first example of strict superadditivity of the identification capacity $C_{\mathrm{ID}}$.
CommentsFirst version, comments are welcome :)
