We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

中文翻译：

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经典和量子信息同时传输的一次性容量界限

我们在称为一次性模型的最通用信道模型下研究量子信道的通信能力。与只能用于传输经典信息（比特）的经典信道不同，量子信道可用于传输经典信息、量子信息（量子比特）以及经典和量子信息的同时传输。在这项工作中，我们研究了量子通道同时传输比特和量子比特的一次性能力。这个问题是在无记忆信道的渐近机制中研究的，其中报告了容量区域的正则化特征。众所周知，私有经典信息的传输与量子信息传输问题密切相关。我们求助于这个想法，并找到了同时传输公共和私人经典信息的可实现的和反向的界限。然后将经典私有速率转换为量子信息速率导致经典和量子信息同时传输的速率区域。在渐近 iid 设置的情况下，我们的一次性结果将评估为文献中的已知结果。我们在可实现性证明中使用的主要工具是基于位置的解码和凸分裂引理。我们的一次性结果被评估为文献中的已知结果。我们在可实现性证明中使用的主要工具是基于位置的解码和凸分裂引理。我们的一次性结果被评估为文献中的已知结果。我们在可实现性证明中使用的主要工具是基于位置的解码和凸分裂引理。