9 problems

Christandl–Ferrara–Lancien's conjecture. There should exist a universal constant $\kappa$ and a function $g:[0,1]\to\mathbb{R}_+$ with

Let $(\mathcal{M}_n)_n$ be a family of sets of quantum states satisfying Axioms 1--5 in Section, and let $D^\infty_{\mathcal{M}}(\rho)$ denote the corresponding regularised relativ…

Centered gamma moment-generating-function conjecture. For every $n$, $k$, and $P$,

Concentration conjecture. There are positive constants $c_1$ and $c_2$ such that for every $n$, $k$, $P$, and $\varepsilon\geq 0$,

Let $P$ be a distribution on a finite alphabet of size $k$, let $\hat{P}_{n,k}$ be its empirical distribution from $n$ independent samples, and let $D(\hat{P}_{n,k} \| P)$ denote t…

Let $P$ be a distribution on a finite alphabet of size $k$, let $\hat{P}_{n,k}$ be its empirical distribution from $n$ independent samples, and let $D(\hat{P}_{n,k} \\| P)$ denote…

Complex relative entropy principle. For each positive subsequence, the limit points of the normalized critical complex entropies are contained in the real parts of the critical val…

Let $d\geq 2$ and let $M(\Delta,d)$ denote the penalty function defined by the minimization over pairs of distributions with entropy difference $\Delta$. For $\Delta\in[0,\log d]$,…

Let $\omega_1$ and $\omega_2$ be states, let $S(\omega_1\Vertomega_2)$ denote their quantum relative entropy, and let $\mathrm{M}(\omega_1\precomega_2)$ be the set of measurement schem…