Many-body chirality for Z_d^(k) stabilizer states equals mirror non-invariance of anyon data, is intrinsically four-partite, and states with d>2 also show intrinsic imaginarity not removable by local unitaries.
The Witt group of non-degenerate braided fusion categories
11 Pith papers cite this work, alongside 11 external citations. Polarity classification is still indexing.
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Pith papers citing it
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abstract
We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid of non-degenerate braided fusion categories modulo the submonoid of the Drinfeld centers and show that its formal properties are similar to those of the classical Witt group.
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representative citing papers
Develops K-theoretic obstruction theory for linearizing QCA representations over arbitrary fields, extracting universal classes and computing homotopy types over point/line/plane in the complex unitary case.
A new framework maps microscopic inputs to universal properties of generic symmetry-enriched TQSLs and establishes a bijective crystalline equivalence principle between lattice-plus-internal and internal-only symmetry data.
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left-right symmetries and boundary conditions in 2D CFTs.
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
Pauli stabilizer codes are classified via algebraic L-theory, yielding a bulk-boundary map to Clifford QCAs and a structural comparison with continuum framed TQFTs.
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
Defines NI-SETOs as relative centers of unitary fusion categories and shows they can be realized in string net models and on boundaries of 3D Walker-Wang models.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
citing papers explorer
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Many-body chirality of topological stabilizer states
Many-body chirality for Z_d^(k) stabilizer states equals mirror non-invariance of anyon data, is intrinsically four-partite, and states with d>2 also show intrinsic imaginarity not removable by local unitaries.
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$K$-Theoretic Obstructions to Linearizing QCA Representations
Develops K-theoretic obstruction theory for linearizing QCA representations over arbitrary fields, extracting universal classes and computing homotopy types over point/line/plane in the complex unitary case.
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Microscopic universal theory of symmetry-enriched topological quantum spin liquids
A new framework maps microscopic inputs to universal properties of generic symmetry-enriched TQSLs and establishes a bijective crystalline equivalence principle between lattice-plus-internal and internal-only symmetry data.
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Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left-right symmetries and boundary conditions in 2D CFTs.
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Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
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Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
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Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
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The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise
Pauli stabilizer codes are classified via algebraic L-theory, yielding a bulk-boundary map to Clifford QCAs and a structural comparison with continuum framed TQFTs.
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Notes on (-2)-form symmetries
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
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Non-invertible symmetry enriched string net topological orders
Defines NI-SETOs as relative centers of unitary fusion categories and shows they can be realized in string net models and on boundaries of 3D Walker-Wang models.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.