论文标题
关于协变量量子误差校正的新观点
New perspectives on covariant quantum error correction
论文作者
论文摘要
协变量代码是量子代码，因此逻辑系统上的对称转换可以通过物理系统上的对称转换来实现，通常具有执行量子误差校正的能力有限（重要的情况是Eastin-nill定理）。在物理的各个领域，包括易于断层的量子计算，凝结物理物理学和量子重力，需要理解协变量量子误差校正的极限。在这里，我们从量子计量学和量子资源理论的角度探索了相对于连续对称性的协变量误差校正，并在这些以前不同的领域之间建立了牢固的联系。我们证明了协变量误差校正的不忠行为的新的和强大的下限，这不仅扩大了以前的NO-GO结果的范围，而且还提供了对现有界限的实质性改善。明确的下限是针对擦除和去极化噪声的。我们还提出了一种几乎使这些下限饱和的协变量代码。
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an important case being the Eastin--Knill theorem). The need for understanding the limits of covariant quantum error correction arises in various realms of physics including fault-tolerant quantum computation, condensed matter physics and quantum gravity. Here, we explore covariant quantum error correction with respect to continuous symmetries from the perspectives of quantum metrology and quantum resource theory, establishing solid connections between these formerly disparate fields. We prove new and powerful lower bounds on the infidelity of covariant quantum error correction, which not only extend the scope of previous no-go results but also provide a substantial improvement over existing bounds. Explicit lower bounds are derived for both erasure and depolarizing noises. We also present a type of covariant codes which nearly saturates these lower bounds.
