Separability transitions in topological states induced by local decoherence

• URL: http://arxiv.org/abs/2309.11879v2
• Date: Wed, 10 Apr 2024 05:46:09 GMT
• Title: Separability transitions in topological states induced by local decoherence
• Authors: Yu-Hsueh Chen, Tarun Grover,
• Abstract summary: We study states with intrinsic topological order subjected to local decoherence from the perspective of separability. We focus on toric codes and the X-cube fracton state and provide evidence for the existence of decoherence-induced separability transitions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 (SRE) 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 SRE states for $p > p_c$, where $p_c$ is related to the paramagnetic-ferromagnetic transition in the 2d (3d) random-field bond Ising model along the Nishimori line.

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