  Let $\mathcal{M}$ be a finite von Neumann algebra and $u_1,\dots,u_N$ be
unitaries in $\mathcal{M}$. We show that $u_1,\dots,u_N$ freely generate
$L(\mathbb{F}_N)$ if and only if $$\left\|\sum_{i=1}^N u_i \otimes
(u_i^{\mathrm{op}})^* + u_i^*\otimes
u_i^{\mathrm{op}}\right\|_{\mathcal{M}\overline{\otimes}\mathcal{M}^{\mathrm{op}}}
= 2\sqrt{2N - 1}.$$
