4 problems

Let $q$ be the alphabet size, let $\mathcal{C}_1$ and $\mathcal{C}_2$ be the uniformly random codes, and let $\psi_{\mathcal{C}_1,\mathcal{C}_2}$ denote their star-product map. Let…

Let a Haar random code be the code obtained by applying an $n$-qubit Haar random unitary to a $k$-qubit input together with $n-k$ ancilla qubits initialized to $\ket{0^{n-k}}$. An…

Let a collection of linear codes be called product-expanding when the associated product code has the product-expansion property used in the paper. The product-expansion conjecture…

Let $E_{\text{ut}}^{\text{ub}}(R,E_{0})$ denote the upper-tail exponent, and suppose that it is truncated to $R$ for relatively high $E_{0}$. Truncation conjecture. This truncation…