One-shot quantum error correction of classical and quantum information
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Abstract
The major goal of quantum communication theory is to determine how much information can be protected from a given quantum noise by encoding operations. The capacity theorems provide answers to the question in various settings. We here provide a capacity theorem when the information to be protected is both classical and quantum, i.e., hybrid information, with assistance of a limited resource of entanglement in one-shot scenario. The theorem covers broad situations, and most capacity theorems in the literature directly follow by simple reductions. Furthermore, we numerically argue that a demonstration of encoding hybrid information by short random quantum circuits is within the reach of near-term quantum technologies. The result bridges a gap between the theoretical progress and the near-future quantum technology in quantum channel coding.