Li Gao

We consider the class of Davies quantum semigroups modelling thermalization for translation-invariant Calderbank-Shor-Steane (CSS) codes in D dimensions, as well as for the two-dimensional Abelian quantum double models. We prove that conditions of Dobrushin-Shlosman-type on the quantum Gibbs state imply a modified logarithmic Sobolev inequality with a constant that is uniform in the system’s size. This is accomplished by generalizing parts of the classical results on thermalization by Stroock, Zegarlinski, Martinelli, and Olivieri to the quantum setting. The results in particular imply the rapid thermalization at any positive temperature for the toric code and Abelian double models in 2D and of the star part of the toric code in 3D, implying a rapid loss of stored quantum information for these models.

The random unitary group channels are in general non-degradable. We give upper and lower bounds on their quantum capacity, which differ only up to a factor 2. Our method relies heavily on operator space tools, in particular complex interpolation.