Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
Higher-form anomaly and long-range entanglement of mixed states
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
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UNVERDICTED 6representative citing papers
Introduces a local one-point fidelity correlator to define SW-SSB, preserving key features like channel stability and long-range conditional mutual information while enabling detection in large and thermodynamic-limit systems.
The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
A counting argument shows the translation-symmetric fixed-point strong-to-weak SSB mixed state is long-range entangled and cannot be expressed as a mixture of short-range entangled states.
For finite 1-form symmetries in (2+1)D, onsiteability holds exactly when the 't Hooft anomaly meets an algebraic condition allowing 1-gauging; the symmetry can then be realized as transversal Pauli operators via ancillas and circuits.
SW-SSB extends symmetry breaking to mixed states and serves as a unifying perspective connecting topological orders, emergent hydrodynamics, and information-theoretic characterizations of phases in open systems.
citing papers explorer
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Invariants of Sequential Circuits and Generalized Non-Abelian Statistics
Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
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Local Strong-to-Weak Spontaneous Symmetry Breaking
Introduces a local one-point fidelity correlator to define SW-SSB, preserving key features like channel stability and long-range conditional mutual information while enabling detection in large and thermodynamic-limit systems.
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Mixed-State Long-Range Entanglement from Dimensional Constraints
The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
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Translation symmetry-enforced long-range entanglement in mixed states
A counting argument shows the translation-symmetric fixed-point strong-to-weak SSB mixed state is long-range entangled and cannot be expressed as a mixture of short-range entangled states.
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Onsiteability of Higher-Form Symmetries
For finite 1-form symmetries in (2+1)D, onsiteability holds exactly when the 't Hooft anomaly meets an algebraic condition allowing 1-gauging; the symmetry can then be realized as transversal Pauli operators via ancillas and circuits.
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Strong-to-Weak Spontaneous Symmetry Breaking
SW-SSB extends symmetry breaking to mixed states and serves as a unifying perspective connecting topological orders, emergent hydrodynamics, and information-theoretic characterizations of phases in open systems.