7 problems

Detectability redundancy conjecture. The detectability condition in Theorem is redundant: if $(\Gamma,\Pi,\hat{\Sigma})$ solves the optimization in, then…

Constrained minimum output entropy conjecture. For every $n\in\mathbb{N}$, $\rho$ and $\kappa\ge1$,

Let $n\in\mathbb{N}$, and let $\hat{\rho}$ be a finite-entropy state of an $n$-mode Gaussian quantum system. Let $g$ be the entropy function for a single-mode thermal Gaussian stat…

The $p\to q$ norm conjecture. For any $\kappa\ge1$ and any $p,q\ge1$, every quantum state $\hat\rho$ satisfies

Let … with entropy $S=S_0>0$, let $^{\operatorname{th}}_{g^{-1}(S_0)}$ denote the thermal state with the same entropy. Infinitesimal minimum output entropy conjecture. The entropy…

Auxiliary-variable conjecture. There exists a random variable $V$ such that $Y_1\to Y_0\to V$ and

Let $h,p,v\in\mathbb{R}_+$, let $X_1^G\sim\mathcal{N}(0,p)$ and let $Z\sim\mathcal{N}(0,v)$ be independent of $X_1^G$. Let $X$ and $X_1$ be i.i.d. random variables with mean $0$ an…