Nonabelian anyon superselection sectors violate Haag duality and its equivalent uniqueness of purifications, as proven by operator algebraic methods and instantiated in Levin-Wen models.
Distillability and positivity of partial transposes in general quantum field systems
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B can steer A relative to a pure state exactly when a state-preserving conditional expectation maps B' onto A.
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A nonabelian anyon violates Haag duality
Nonabelian anyon superselection sectors violate Haag duality and its equivalent uniqueness of purifications, as proven by operator algebraic methods and instantiated in Levin-Wen models.
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Quantum steering is equivalent to state-preserving conditional expectations
B can steer A relative to a pure state exactly when a state-preserving conditional expectation maps B' onto A.