15 problems

Let $\vec{Q}$ be a distribution in the four-party star network. Say that $\vec{Q}$ passes the factorisation star-shaped trilocal NPA hierarchy if, for every integer $n\geq 4$, ther…

Consider the four-party star network and a hierarchy of Factorisation Star-shaped Trilocal Moment Matrices, whose existence implies that a distribution is an Anti-state Commutator…

Let $\vec{Q}=\{q(abc|xyz)\}$ be a distribution in the bilocal scenario. Say that $\vec{Q}$ passes the bilocal inflation-NPA hierarchy when it satisfies the hierarchy of compatible…

Let the factorisation bilocal hierarchy and the inflation-NPA hierarchy be the two hierarchies of tests for bilocal quantum distributions described in the paper. Inflation-NPA comp…

Continuity conjecture for $C_B^{\infty}$. The analogue of the continuity condition in Proposition B should hold for the function $C_B^{\infty}$.

Partial distinguishability affects many-particle interference patterns, and one seeks tractable measures that capture this distortion. Higher-order-correlation conjecture. Higher-o…

Let the set of quantum correlations consist of the correlations obtainable from finite-dimensional quantum systems, and let the set of quantum commuting correlations consist of tho…

Let $P_\mathrm{II*}$ be the selected set of Level-II partial separability properties, and let … be the set of nonempty filters. For each filter…

Nontriviality conjecture. $\underline{\boldsymbol{\xi}}$-separability is nontrivial for every $\underline{\boldsymbol{\xi}}\in P_\mathrm{III*}$; equivalently,

Let $\rho^{AB}$ be a bipartite quantum state, and let $\rho^{ABC}$ range over tripartite quantum states satisfying … For local observables $O_A$ and $O_B$, let…

Grover's search algorithm searches for $m$ targets in a database of size $N$, using quantum operations with appropriately adjusted phases to obtain a speedup over classical search.…

Let $d$ be the number of fermionic modes, and let $B=[b_k^n]$ be the matrix whose entries are the coefficients appearing in the characterization of $\mathrm{Spin}(2d)$-invariant bi…

Let $\rho_{AB}$ be a two-mode Gaussian state with covariance matrix in standard form, and let $Q_{\mathcal{N}}(\rho_{AB})$ denote its negativity of quantumness, optimized over loca…

Let a doubly' quantized theory be a theory of the type considered in the source, with CHSH correlations and CHSH bound defined in the usual way. Doubly quantized theory conjecture.…

Let $\rho_{AB}$ be a bipartite state, and let a local measurement produce a post-measurement state. Write $I(\rho_{AB})$ for the mutual information of the state before measurement…