8 problems

Let a qubit permutation-invariant quantum error-correcting code correct errors of weight at most $t$, and let $n_{\rm min}(t)$ denote the smallest block length among such codes. Th…

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…

Optimality conjecture. The sum of the numbers obtained by this code construction is optimal.

Extremality conjecture. If a $[[n,0,d]]$ stabilizer code achieves the maximal concentratable entanglement on $n$ qubits, then it must be an extremal code.

Essential attainability conjecture. For sufficiently large alphabet size $q$, all integer points below the line connecting MDS and EAQ correspond to possible code values.

Let $q$ be the local dimension, and let a linear $[[n,n-2d+2,d]]_q$ quantum MDS code have length $n$, dimension parameter $n-2d+2$, and minimum distance $d$. MDS conjecture. If … a…

Entanglement-assisted stabilizer codes use maximally entangled states, or ebits, to import classical binary or quaternary linear codes into the quantum setting. The entanglement-as…

In quantum information, phase-shift errors and qubit-flip errors are two types of errors affecting qubits. Phase-shift error conjecture. It is conjectured that phase-shift errors o…