There exist a noncommutative probability space $(\mathcal{A}, \tau)$, self-adjoint elements $a,b,c,d \in \mathcal{A}$, and a noncommutative polynomial $p \in \mathbb{C}\langle X,Y\rangle$ in two noncommuting indeterminates $X$ and $Y$ such that, for every positive integer $n$,
Equivalently, the joint laws of the pairs $(a,b)$ and $(c,d)$, defined as the linear functionals $r \mapsto \tau(r(a,b))$ and $r \mapsto \tau(r(c,d))$ from $\mathbb{C}\langle X,Y\rangle$ to $\mathbb{C}$, are different.