Decohered color code and emerging mixed toric code by anyon proliferation: Topological entanglement negativity perspective

• URL: http://arxiv.org/abs/2604.22521v2
• Date: Thu, 30 Apr 2026 06:57:35 GMT
• Title: Decohered color code and emerging mixed toric code by anyon proliferation: Topological entanglement negativity perspective
• Abstract summary: We study how the color code under decoherence gives rise to an intrinsic mixed-state topological order (imTO)<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 ${\rm TEN} = 2 \ln 2$, the maximally decohered state has ${\rm TEN} = \ln 2$, indicating emergence of a single toric code. By tuning the decoherence strength, we find a smooth crossover in TEN accompanied by a pronounced, nearly system-size-independent peak in its variance. We further show that the negativity exhibits characteristic scaling only for subsystem partitions commensurate with the triangular lattice of the emergent toric code. Our results demonstrate that negativity-based quantities provide powerful probes of mixed-state topological order generated by decoherence.

Related papers

• Nonlocality-induced critical-length hierarchy from non-Hermitian competition [48.9823527611878]
  In short-range systems formed by two coupled chains, competition leads to the critical-length law $N_csimln D$.<n>Here we show that long-range hoppings fundamentally reorganizes this critical behavior, producing a hierarchy of distinct scaling laws.<n>Our results offer a platform-independent framework testable in programmable topoelectrical circuits, photonic lattices and digital quantum simulators.
  arXiv  Detail & Related papers  (2026-08-03T18:00:18Z)
• Microscopic study of topological phase transitions: Percolation point of view [0.0]
  We investigate microscopic mechanisms underlying decoherence-induced transitions between topologically ordered states.<n>In a first case study, we analyze the color code using topological entanglement negativity (TEN) and a disorder parameter associated with 1-form symmetry.<n>We introduce quasi-local TEN (QLTEN), which visualizes the spatial distribution of local topological properties and the growth of decohered regions.<n>As a second case study, we consider the toric code on a triangular lattice under external-field-type decoherence.
  arXiv  Detail & Related papers  (2026-07-29T09:53:17Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Topological quantum color code model on infinite lattice [1.715412829836753]
  The color code model is a crucial instance of a Calderbank--Shor--Steane (CSS)-type topological quantum error-correcting code.<n>From the perspective of quantum phases of matter, it is essential to understand these excitations in the thermodynamic limit.<n>We show that the order of the color code is described by $mathsfRep(D(mathbbZ_2)) simeq mathsfRep(D(mathbbZ_2)$, which is equivalent to a double layer of the toric code
  arXiv  Detail & Related papers  (2026-01-18T13:53:18Z)
• Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
  We show topologically ordered states in the complex-valued spectra of non-Hermitian systems.<n>These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated.<n>We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
  arXiv  Detail & Related papers  (2024-10-24T10:16:47Z)
• Understanding Heterophily for Graph Neural Networks [42.640057865981156]
  We present theoretical understandings of the impacts of different heterophily patterns for Graph Neural Networks (GNNs) We show that the separability gains are determined by the normalized distance of the $l$-powered neighborhood distributions. Experiments on both synthetic and real-world data verify the effectiveness of our theory.
  arXiv  Detail & Related papers  (2024-01-17T11:01:28Z)
• Separability transitions in topological states induced by local decoherence [0.0]
  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.
  arXiv  Detail & Related papers  (2023-09-21T08:28:17Z)
• Intrinsic Mixed-state Topological Order [4.41737598556146]
  We show that decoherence can give rise to new types of topological order.<n>We construct concrete examples by proliferating fermionic anyons in the toric code via local quantum channels.<n>The resulting mixed states retain long-range entanglement, which manifests in the nonzero topological entanglement negativity.
  arXiv  Detail & Related papers  (2023-07-25T18:34:10Z)
• Quantum phase transitions in the $K$-layer Ising toric code [0.0]
  Investigation of the $K$-layer Ising toric code corresponding to $K$ layers of two-dimensional toric codes coupled by Ising interactions. For small Ising interactions the system displays $mathbbZK$ topological order originating from the toric codes in each layer. The latter is demonstrated for general $K$ by deriving an effective low-energy model in $Krm th$-order perturbation theory. Extrapolation of the elementary energy gaps gives convincing evidence that the ground-state phase diagram consists of a single quantum critical point in the
  arXiv  Detail & Related papers  (2022-01-25T15:14:23Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.