  We prove the following operator-coefficients free Poincar\'{e} inequality:
$$|f(X)-E[f(X)]|_{2}\leq2|X|_{2}\|\widehat{\partial}_{X:B}[f(X)]\|_{\pi}, \quad
f(X) \in \mathrm{dom}(\widehat{\partial}_{X:B}),$$ where $\|\cdot\|_{\pi}$ is
the projective tensor norm.
