Efficient learning of Clifford disentanglers and typical $t$-doped unitaries with exponentially more $T$ gates

Highly entangled and highly non-stabilizer quantum states need not be hard to learn. We give efficient algorithms for testing and recovering hidden tensor-product structure in unknown pure state vectors of the form $\lvertψ\rangle = U_C \bigotimes_i \lvertψ_i\rangle$, where $U_C$ is an arbitrary unk