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A Decoupling Approach to Classical Data Transmission Over Quantum Channels

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3 Author(s)
Frédéric Dupuis ; ETH Zurich, Zürich, Switzerland ; Oleg Szehr ; Marco Tomamichel

Most coding theorems in quantum Shannon theory can be proven using the decoupling technique. To send data through a channel, one guarantees that the environment gets no information about it. Uhlmann's theorem then ensures that the receiver must be able to decode. While a wide range of problems can be solved this way, one of the most basic coding problems remains impervious to a direct application of this method, sending classical information through a quantum channel. We will show that this problem can, in fact, be solved using decoupling ideas, specifically by proving a dequantizing theorem, which ensures that the environment is only classically correlated with the sent data. Our techniques naturally yield a generalization of the Holevo-Schumacher-Westmoreland theorem to the one-shot scenario, where a quantum channel can be applied only once.

Published in:

IEEE Transactions on Information Theory  (Volume:60 ,  Issue: 3 )