New perspectives on covariant quantum error correction

Covariant codes are quantum such that a symmetry transformation on the logical system could be realized by physical system, usually with limited capability of performing error correction (an important case being Eastin–Knill theorem). The need for understanding limits covariant arises in various realms physics including fault-tolerant computation, condensed matter and gravity. Here, we explore respect to continuous symmetries from perspectives metrology resource theory, establishing solid connections between these formerly disparate fields. We prove new powerful lower bounds infidelity correction, which not only extend scope previous no-go results but also provide substantial improvement over existing bounds. Explicit derived both erasure depolarizing noises. present type nearly saturates