Quantum random walks and vanishing of the second Hochschild cohomology

Given a conditionally completely positive map $mathcal L$ on a unital $ast$-algebra $A$, we find an interesting connection between the second Hochschild cohomology of $A$ with coefficients in the bimodule $E_{mathcal L}=B^a(A oplus M)$ of adjointable maps, where $M$ is the GNS bimodule of $mathcal L$, and the possibility of constructing a quantum random walk (in the sense of cite{AP,LP,L,KBS}) corresponding to $mathcal L$.