Citation: Wang, Zijian, Zhengzhi Wu, and Zhong Wang. "Intrinsic mixed-state topological order without quantum memory." arXiv preprint arXiv:2307.13758 (2023).
Web: https://arxiv.org/abs/2307.13758v2
Tags: Toric-code, Phase-transition, Generalized-symmetries
In this paper, the authors describe a new type of topological order which is inherently based on mixed-states. The idea is quite simple. Suppose one starts with the toric code and applies quantum channels which proliferate fermions at every edge with probability 1/2. This has the effect of "condensing" the fermion. However, only bosons can condense and thus something must have gone wrong! What has gone wrong is that the resulting mixed state is some new sort of strange topological order which looks like the toric code with a gauged fermion.
In general, it seems like there is a whole zoo of exotic topological phases for which there are only mixed state wave functions, and no pure state wave functions. This sort of mixed state topological is interesting and has all sorts of potential consequences.
There is an algebraic theory of mixed state topological order, in terms of premodular categories and classical gauging of anomalous symmetries:
> Wang, Zijian, Zhengzhi Wu, and Zhong Wang. "Intrinsic mixed-state topological order without quantum memory." arXiv preprint arXiv:2307.13758 (2023).