4 problems

LOCC hierarchy conjecture. For all $\underline{\boldsymbol{\alpha}},\underline{\boldsymbol{\beta}}\in P_\text{III}$,

Nonemptiness conjecture. The classes indexed by $P_\text{III}$ are all nonempty; equivalently,

Consider a pure state $\psi^{C_1C_2\ldots C_mAB}$ shared by helpers $C_1,\ldots,C_m$ and recipients Alice and Bob. In the standard multiple-blocking proof, each helper performs ran…

Let $s$ be the message encoded in the shared state, and let an LOCC protocol use an unlimited number of communication rounds. The protocol's output has mutual information with $s$,…