Golden-Thompson via pinching inequality

Abstract

For two hermitian matrices $A$ and $B$, Golden-Thompson inequality \cite{golden1965lower, thompson1965inequality} states that $$ \mathrm{tr}\left[ \exp{(A+B)} \right] \leq \mathrm{tr}\left[ \exp{(A)}\exp{(B)} \right]. $$ We elaborate here the proof from Sutter et al. (2017).