Classification and Exact Local Masking in Finite-Field Clifford Dual-Unitary Circuits

Abstract

We classify two-qudit Clifford dual-unitary gates over the finite field $\mathbb{F}_q$, where the local dimension $q$ is a prime power, and apply the classification to exact local masking and operator transport in homogeneous brickwork circuits. Under ordered one-qudit Clifford equivalence, the dual-unitary locus contains $q-2$ perfect-tensor cores, one rank-one core, and one SWAP core. Homogeneous repetition separates these cores into five distinct transport phases. The one-site Weyl edge channels determine exact local-masking distances. Writing $d_r(t)$ for the masking distance against output observers controlling at most $r$ sites, perfect-tensor circuits attain \[ d_1(t)=4t, \qquad d_2(t)=4t-2, \] whereas delayed erasers satisfy \[ d_1(t)=4t-2, \qquad d_2(t)=4t-4 \] for $t\geq 2$. Consequently, sufficiently short quantum messages are completely hidden from every one- or two-qudit output subsystem, even when the input is entangled with a reference, while remaining exactly recoverable from the full output. For $q=3$, we construct an explicit perfect-tensor Clifford gate from two inverse SUM gates. Exhaustive Weyl-support searches for $t=1,2,3$ reproduce the predicted masking distances. For a coherent perturbation of this gate, local leakage scales linearly with the perturbation strength, whereas the infidelity of recovery using the ideal inverse scales quadratically near the perfect point.