Chen Yu-Hsueh, Grover Tarun
Department of Physics, University of California at San Diego, La Jolla, California 92093, USA.
Phys Rev Lett. 2024 Apr 26;132(17):170602. doi: 10.1103/PhysRevLett.132.170602.
We study states with intrinsic topological order subjected to local decoherence from the perspective of separability, i.e., whether a decohered mixed state can be expressed as an ensemble of short-range entangled pure states. We focus on toric codes and the X-cube fracton state and provide evidence for the existence of decoherence-induced separability transitions that precisely coincide with the threshold for the feasibility of active error correction. A key insight is that local decoherence acting on the "parent" cluster states of these models results in a Gibbs state. As an example, for the 2D (3D) toric code subjected to bit-flip errors, we show that the decohered density matrix can be written as a convex sum of short-range entangled states for p>p_{c}, where p_{c} is related to the paramagnetic-ferromagnetic transition in the 2D (3D) random bond Ising model along the Nishimori line.
我们从可分性的角度研究具有内在拓扑序且受到局部退相干影响的态，即退相干后的混合态是否能表示为短程纠缠纯态的系综。我们聚焦于环面码和X立方分数子态，并为存在退相干诱导的可分性转变提供了证据，这些转变恰好与主动纠错可行性的阈值重合。一个关键的见解是，作用于这些模型的“母”簇态上的局部退相干会导致一个吉布斯态。例如，对于受到比特翻转错误影响的二维（三维）环面码，我们表明当(p > p_{c})时，退相干后的密度矩阵可以写成短程纠缠态的凸和，其中(p_{c})与沿着西森线的二维（三维）随机键伊辛模型中的顺磁 - 铁磁转变有关。
