Nuclear Toeplitz operators between Fock spaces

We characterize the nuclearity of Toeplitz operators $T_{\mu }:F_{\alpha }^p\to F_{\alpha }^q$ with Borel measure symbols for $1\le p,q\le \mathrm{\infty }$. For positive measures $\mu$ and $q\le p$, we provide necessary and sufficient conditions in terms of the Berezin transform and establish a rigidity property for nuclearity across this range. In the case $p<q$, we obtain separate necessary and sufficient conditions, indicating that the Berezin transform alone is insufficient for a complete characterization. Our results extend to Fock spaces on ${\mathbb{C}}^n$.