Two-dimensional topological order is a robust quantum memory to local errors. The memory exhibits a finite error threshold below which the encoded information can be protected using error correction algorithms. The error threshold suggests the existence of distinct error-induced phases, however, the threshold depends on the algorithm and is not intrinsic to the quantum state. In this talk, I will propose intrinsic characterizations of error-induced phases in topological order subject to local errors. I first introduce the errorfield double formalism and map the error-induced phases to (1+1)D boundary phases of topologically ordered systems. These phases cannot be detected by observables in a single-copy density matrix and instead are only probed by information-theoretical quantities. Next, I will introduce three complementary diagnostics of such phases: (1) quantum relative entropy between an error-corrupted ground state and excited state; (2) coherent quantum information; (3) topological entanglement negativity. I will discuss these results in concrete examples.
Host: Meng Cheng (m.cheng@yale.edu)