One-shot quantum error correction of classical and quantum information

TL;DR

This paper presents a general capacity theorem for one-shot quantum error correction of both classical and quantum information, demonstrating its feasibility in random circuits and intrinsic nature in chaotic systems.

Contribution

It introduces a broad, applicable capacity theorem for hybrid information with limited entanglement assistance in one-shot scenarios, extending prior results.

Findings

QEC demonstrated by short random quantum circuits is feasible.

QEC is intrinsic in quantum chaotic systems.

The results connect quantum information theory with fundamental physics.

Abstract

Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly applicable form of capacity theorem for both classical and quantum information, i.e., hybrid information, with assistance of a limited resource of entanglement in one-shot scenario, which covers broader situations than the existing ones. Harnessing the wide applicability of the theorem, we show that a demonstration of QEC by short random quantum circuits is feasible and that QEC is intrinsic in quantum chaotic systems. Our results bridge the progress in quantum information theory, near-future quantum technology, and fundamental physics.