Mixed-state TQFTs
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.
Cite
@article{arxiv.2110.13946,
title = {Mixed-state TQFTs},
author = {Modjtaba Shokrian Zini and Zhenghan Wang},
journal= {arXiv preprint arXiv:2110.13946},
year = {2021}
}