9 problems

Let $\rho_\beta$ be a reduced density matrix on a subsystem, and consider the cluster-expansion method applied to the logarithm of reduced density matrices in order to compute cond…

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…

Completely contractive data-processing conjecture for conditional mutual information. For any channel $\mathcal{E}:C\rightarrow C'$ with trivial correctable algebra, there exists a…

Generic MPDO conjecture. For a generic' MPDO, there exists a constant $c>0$ such that for any tripartition $ABC$ in which $B$ separates $A$ from $C$ by distance $\ell$,

Let $\mathcal{X}$ be a domain, let $\mathcal{W}$ be a class of functions $f:\mathcal{X}\to\{0,1\}$ with VC dimension $d\geq 1$, and let $n\geq 1$. For a dataset…

Let $\mathcal{X}$ be a domain, let $\mathcal{W}$ be a class of functions $f:\mathcal{X}\to\{0,1\}$ with VC dimension $d\geq 1$, and let $n\geq 1$. For a dataset…

Let $\mathcal{X}$ be a domain, let $\mathcal{W}$ be a class of functions $f:\mathcal{X}\to\{0,1\}$ with VC dimension $d\geq 1$, and let $n\geq 1$. For a dataset…

Let $\rho_{ABC}\in\mathcal{S}(\mathcal{H}_{ABC})_{++}$, $\tau_{AC}\in\mathcal{S}(\mathcal{H}_{AC})_{++}$, $\theta_{BC}\in\mathcal{S}(\mathcal{H}_{BC})_{++}$, and…