On the near-optimality of one-shot classical communication over quantum channels

Abstract

We study the problem of transmission of classical messages through a quantum channel in several network scenarios in the one-shot setting. We consider both the entanglement assisted and unassisted cases for the point to point quantum channel, quantum multiple-access channel, quantum channel with state and the quantum broadcast channel. We show that it is possible to near-optimally characterize the amount of communication that can be transmitted in these scenarios, using the position-based decoding strategy introduced in a prior work [Anshu, Jain and Warsi, 2017]. In the process, we provide a short and elementary proof of the converse for entanglement-assisted quantum channel coding in terms of the quantum hypothesis testing divergence (obtained earlier in [Matthews and Wehner, 2014]). Our proof has the additional utility that it naturally extends to various network scenarios mentioned above. Furthermore, none of our achievability results require a simultaneous decoding strategy, existence of which is an important open question in quantum Shannon theory.

arXiv comment20 pages, version 1

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• Quantum teleportation with relativistic communication from first principles
• One-shot quantum error correction of classical and quantum information
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• Efficient methods for one-shot quantum communication
• One-Shot Triple-Resource Trade-Off in Quantum Channel Coding
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