Quantum information theory and quantum error correction fundamentals

Yoshifumi Nakata, Eyuri Wakakuwa, Hayata Yamasaki

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 the assistance of a limited resource of entanglement in a 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.

Jincheng Zhang

Quantum error correction (QEC) is widely regarded as the indispensable cornerstone for achieving scalable, fault-tolerant quantum computation. However, conventional fault-tolerance theorems traditionally rely on abstract circuit models that frequently abstract away fundamental physical laws, treating noise channels and error syndromes as purely mathematical parameters. In this paper, we establish the Physical Limit of Quantum Error Correction (PLQEC) framework, investigating whether there exists an absolute, nature-imposed lower bound on the residual error probability, denoted as p_min, below which reliable quantum information preservation becomes physically unattainable due to deeply rooted thermodynamic, informational, and spacetime constraints. By systematically integrating Landauer's principle, von Neumann entropy bounds, the intrinsic thermodynamics of quantum measurement, and holographic gravity principles, we derive universal fundamental limits on quantum error correction thresholds. We demonstrate that physical constraints such as minimal energy dissipation per syndrome extraction cycle, quantum speed limits, decoherence velocities, and spacetime curvature cutoffs impose strict, unyielding boundaries on fault-tolerant quantum architectures. This work bridges the profound gap between abstract quantum information theory and fundamental physical law, opening a new frontier in understanding the ultimate operational boundaries of quantum information processing in our physical universe.

Ivan B. Djordjević

Ivan B. Djordjević

Jincheng Zhang

Quantum error correction (QEC) is a critical component of quantum computing, enabling the reliable transmission and manipulation of quantum information. However, QEC is inherently probabilistic, demanding precise calibration and potentially vulnerable to decoherence. This paper investigates the use of probability theory to analyze and improve the robustness of QEC protocols. We propose a novel "self-adaptive correction" algorithm based on quantum state dynamics, dynamically adjusting error correction strategies based on environmental fluctuations. Our core claim is that by applying probabilistic methods to the QEC process, we can achieve improved reliability and efficiency compared to static QEC approaches. This research explores the fundamental concepts of probability, statistical analysis, and dynamic adaptation within the context of quantum information processing. The core mechanism focuses on developing a quantum state-based feedback loop that optimizes error correction based on environmental changes, offering a more flexible and resilient approach. The study highlights the potential of probability theory to enhance the design and implementation of robust QEC protocols.