5 problems

Let $A$, $B$, and $C$ be regions of a quantum system, and let $\rho_\beta$ be a quantum Gibbs state. Suppose … The conditional mutual information is … where $S_{\rho_\beta}(X)$ den…

Let $A$, $B$, and $C$ be regions of a quantum system $\rho_\beta$, with … where $\Lambda$ denotes the entire system. For a tripartite state, define the conditional mutual informati…

Extension conjecture. The conclusions established for the restricted class of Gibbs states and noise channels should hold in these more general cases as well.

Quantum Markov conjecture. For arbitrary quantum Gibbs states,

Quantum Gibbs-state preparation conjecture. The sufficient number of elementary quantum gates for preparing a one-dimensional quantum Gibbs state should also be quasi-linear, as in…