Decohered color code and emerging mixed toric code by anyon proliferation: Topological entanglement negativity perspective
Keisuke Kataoka, Yoshihito Kuno, Takahiro Orito, Ikuo Ichinose

TL;DR
This paper investigates how decoherence affects the color code, leading to an intrinsic mixed-state topological order that resembles a single toric code, characterized by topological entanglement negativity.
Contribution
It introduces a gauging procedure for mixed stabilizer states and demonstrates the emergence of a toric code-like phase under decoherence using topological entanglement negativity.
Findings
Decoherence reduces TEN from 2 ln 2 to ln 2, indicating a transition to a single toric code.
Smooth crossover in TEN observed with varying decoherence strength.
Negativity scaling reveals subsystem partition dependence related to the emergent toric code.
Abstract
We study how the color code under decoherence gives rise to an intrinsic mixed-state topological order (imTO), which has no counterpart in pure ground states of local gapped Hamiltonians. For decoherence induced by XX-type operators on red links of the honeycomb lattice, we show that the resulting mixed state inherits half of the topological properties of the color code, including anyon content, logical operators, and topological entanglement structure. Using a gauging procedure for mixed stabilizer states, we identify the emergent phase as closely related to a single toric code. We characterize this phase by topological entanglement negativity (TEN) and perform efficient stabilizer-formalism simulations. While the pure color code has , the maximally decohered state has , indicating emergence of a single toric code. By tuning the decoherence…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
