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Mixed-state TQFTs
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In this short note, we propose a generalization of Atiyah type TQFTs from pure states to mixed states in the sense that the Hilbert space of pure states associated to a space manifold is replaced by a quantum coherent space related to density matrices. Atiyah type TQFT is a symmetric monoidal functor from the Bord category of manifolds to the category Vec of finite dimensional vector spaces. In this paper, we define mixed-state TQFTs by replacing the target category Vec by QCS--the category of quantum coherent spaces, then a mixed-state TQFT is simply a symmetric monoidal functor from Bord to QCS. We also discuss how to construct interesting examples from subsystem quantum error correction codes beyond the trivial ones--all Atiyah type TQFTs.
Forward citations
Cited by 2 Pith papers
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Tensor Network Representations for Intrinsically Mixed-State Topological Orders
A Choi-state anyon condensation protocol builds fixed-point tensor networks for intrinsic mixed-state topological orders from decohered pure states.
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SymTFT Approach for Mixed States with Non-Invertible Symmetries
A SymTFT-based classification of 1+1d mixed-state phases with non-invertible strong and weak symmetries, with explicit lattice-model examples.
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