Disentangling transitions in topological order induced by boundary decoherence

Abstract

We study the entanglement structure of topological orders subject to decoherence on the bipartition boundary. Focusing on the toric codes in $d$ space dimensions for $d=2,3,4$, we explore whether the boundary decoherence may be able to induce a disentangling transition, characterized by the destruction of mixed-state long-range entanglement across the bipartition, measured by topological entanglement negativity. A key insight of our approach is the connection between the negativity spectrum of the decohered mixed states and emergent symmetry-protected topological orders under certain symmetry-preserving perturbation localized on the bipartition boundary. This insight allows us to analytically derive the exact results of entanglement negativity without using a replica trick.

16 pages, 5 figures; typos fixed

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• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Mixed-State Topological Order under Coherent Noise
• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Holographic duality between bulk topological order and boundary mixed-state order
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity