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Let $G$ be a compact quantum group. We show that given a $G$-equivariant$\mathrm{C}^*$-correspondence, the Pimsner algebra $\mathcal{O}_E$ can benaturally made into a $G$-$\mathrm{C}^*$-algebra. We also provide sufficientconditions under which it is guaranteed that such a $G$-action on the Pimsneralgebra $\mathcal{O}_E$ is a lift, in a suitable sense. When $G$ is of Kactype, a $\mathrm{KMS}$ state on the Pimsner algebra, arising from a quasi-freedynamics, is $G$-equivariant if and only if the tracial state obtained fromrestricting it to the coefficient algebra is $G$-equivariant, under a naturalcondition. We apply these results to the situation when the$\mathrm{C}^*$-correspondence is obtained from a finite, directed graph anddraw various conclusions on the quantum automorphism groups of such graphs,both in the sense of Banica and Bichon.

Equivariant $\mathrm{C}^*$-correspondences and compact quantum group actions on Pimsner algebras