11 problems

Let $n$ be the number of excitations and let the transition matrix be chosen from the Haar ensemble. Consider the operator norm of the map from the $d$-fold bunched subspace back i…

Let $M_{\rm S}$ denote the number of spatial modes, let $\boldsymbol{\boldsymbol{\hat b}}=(\hat b_0,\ldots,\hat b_{M_{\rm S}-1})$ be the transformed modal annihilation operators, a…

Consider estimation of a small transverse displacement using an optimal single-mode Gaussian state, and let the quantum Fisher information (QFI) quantify the attainable information…

A single spatial mode is excited in a Gaussian state, with the state potentially displaced and squeezed. Optimal Gaussian probe conjecture. The optimum Gaussian-state probe is a si…

Unfairness-witness conjecture. The following inequality holds:

QCS loss-threshold conjecture. All states lose their QCS-certified nonclassicality when the loss reaches the maximum value of $50\%$ or more.

A beam splitter transforms an input state in one mode together with the vacuum in the other mode into a two-mode output state. The reflection and transmission probabilities are equ…

Let $V$ be the covariance matrix and let $A^{\pm}_{\rm mix}$ denote the matrix appearing in the condition for Wigner-function negativity. The negativity volume is the integral of t…

Minimum pumped-crystal conjecture. Three pumped crystals are the minimum number required for constructing a desired locally dissipative system.

Zero-distribution conjecture. The number of zeros of $G_\pm(x)$ in each interval $[n,n+1]$, for $n\in\mathbb{N}_0$, is restricted to be $0$, $1$, or $2$. Moreover, an interval…

Universality conjecture. On $k$ modes, these $\binom{k}{3}$ natural embeddings of $O_{3}$ generate $SO(k-1)$.