2 problems

Let $V$ be a passive or active fermionic linear-optics circuit initialized in the state $\left|\Psi_{\mathrm{in}}\right>$, let $\mathbf{x}_0$ be a fiducial outcome, and let…

Fix a constant $p\in(0,1)$. Let $n_t$ and $k_t$ be increasing sequences of positive integers such that $k_t=o(\sqrt{n_t})$ and $k_t$ divides $n_t$, and let … be a sequence of rando…