协变量子纠错的新观点
New perspectives on covariant quantum error correction
摘要：
协变码是这样的量子码，使得逻辑系统上的对称变换可以通过物理系统上的对称变换来实现，通常具有有限的执行量子纠错的能力（一个重要的情况是Eastin-Knill定理）。理解协变量子纠错极限的需要出现在物理学的各个领域，包括容错量子计算、凝聚态物理和量子引力。在这里，我们探讨协变量子纠错与连续对称性的量子精密测量和量子资源理论的角度来看，这些以前不同的领域之间建立坚实的联系。我们证明了新的和强大的下界的不保真度的协变量子纠错，这不仅扩展了以前的不去的结果的范围，但也提供了一个显着的改善现有的界限。明确的下限推导出擦除和去极化噪声。我们还提出了一类几乎饱和这些下界的协变码。
英文摘要：
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.
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