Mixed-state TQFTs

• URL: http://arxiv.org/abs/2110.13946v1
• Date: Sun, 24 Oct 2021 13:53:38 GMT
• Title: Mixed-state TQFTs
• Authors: Modjtaba Shokrian Zini and Zhenghan Wang
• Abstract summary: We propose a generalization of Atiyah type TQFTs from pure states to mixed states. We define mixed-state TQFTs by replacing the target category Vec by QCS.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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