9 problems

Let $G$ be a finite regular graph, and let $H$ be a 2-lift of $G$. An eigenvalue of $H$ not inherited from $G$ is called new, and let $\rho(\mathsf{UCT}(G))$ denote the relevant un…

Let $\rho$ be a quantum state associated with a lifted graph, and let the logarithmic coherence number be defined for pure states by … with the mixed-state measure obtained by conv…

Let $G$ be a graph, let ${{\mathrm{HL}}'_2}^r(G)$ denote its $r$-fold iterated lift, and let the relative entropy of coherence be measured for the corresponding lifted quantum syst…

An $\ell$-lift of $K_n$ is obtained by replacing every vertex of $K_n$ with an independent set of size $\ell$ and every edge with a matching of size $\ell$ between the correspondin…

An $\ell$-lift of a graph $G$ is obtained by replacing every vertex of $G$ with an independent set of size $\ell$, and replacing each edge by a matching of size $\ell$ between the…

Let $H$ be a $d$-regular multigraph on $k$ vertices, and let $\varepsilon>0$. Write $\mathcal{L}_{m}(H)$ for an $m$-sheeted lift of $H$. The operators…

Let $H$ be a $d$-regular graph on $k$ vertices. A graph lift of $H$ with $m$ sheets is denoted by $\mathcal{L}_{m}(H)$, and $\mathcal{G}(km,d)$ denotes a uniformly random $d$-regul…

Let $G$ be a finite graph, and let $H$ be a lift of $G$. Write $\mathsf{spec}(G)$ for the spectrum of $G$, and let $\rho(\mathsf{UCT}(G))$ denote the relevant universal-cover spect…

Ramanujan-lift probability conjecture. There exists a constant $c$ with $0<c<1$ such that