21 problems

A Kochen–Specker (KS) set is a set of rays, or equivalently projectors, together with their orthogonality relations. Such a set is rigid if any set of projectors, not necessarily o…

Let $\mathcal{Q}_1$ and $\mathcal{Q}_2$ be subsystem stabilizer codes, and consider a fault-tolerant code-switching protocol between them. Let the set of transversal gates for each…

Let $\mathcal{M}$ be a measurement cover that realizes a contextual empirical model for some quantum state. A measurement cover is state-independently AvN in a partial closure when…

Partial-closure AvN conjecture. Any measurement cover $\mathcal{M}$ that realizes a contextual empirical model for some state $\psi$ is state-independently $\mathrm{AvN}$ in a part…

Let $d>1$ be an odd integer. A linear system over $\mathbb{Z}_d$ is a system of linear constraints with coefficients and right-hand sides in $\mathbb{Z}_d$; a solution in a group…

The Torpedo Game is a prepare-and-measure game in dimension $d$, where classical strategies assign answers subject to the game's consistency conditions, and a strategy is perfect w…

Noncoordinatization conjecture. The critical Kochen–Specker MMPH 19-5 has no coordinatization from $\{0,\pm1\}$.

Noncoordinatization conjecture. The 7-dimensional MMPH 13-6 has no coordinatization.

Let $l_{cm}$ denote the minimum number of hyperedges that can contain the value $1$ in a considered MMP hypergraph. Rank-of-contextuality conjecture. We conjecture that $l_{cm}$ is…

Filled pentagon minimality conjecture. The filled pentagon MMPH 10-5 is the smallest MMPH with a coordinatization in the 3-dimensional Hilbert space.

A Veldkamp space for $N$-qubits contains Veldkamp lines, and contextual configurations are configurations associated with quantum contextuality. New-contextual-configurations conje…

The canonical double-six configuration of Mermin pentagrams contains $20$ observables, while the $20$-dimensional irreducible representation of $A_5$ has a weight diagram. Double-s…

A Veldkamp space for $N$-qubits has Veldkamp lines, and contextual configurations are configurations that rule out noncontextual hidden-variable theories. Contextual-configuration…

The paper considers the operational information-processing task defined by its parity-oblivious $d$-level random access code protocol, and the associated noncontextuality inequalit…

Contextuality is a property of quantum systems associated with the impossibility of reproducing their measurement statistics using a noncontextual hidden-variable model. Weak value…

Equivalence of the cyclic-system criteria. The master criterion follows from the general cyclic-system criterion as well; equivalently, the two criteria are equivalent. The source…

Let $\left(\mathfrak{S},\mathfrak{C}\right)$ be a system with … where $\pi$ is a circular permutation of $\{1,\ldots,n\}$, and … Here $\Delta_0(\mathfrak{C})$ is the sum of minimal…

The Mermin pentagrams are configurations of commuting four-qubit observables, and their total number is $12096$, equal to the order of $G_2(2)$. The split Cayley hexagon conjecture…

Let $W(5,2)$ be the symplectic polar space whose automorphism group is isomorphic to $Sp(6,2)$. A magic WA-configuration is a configuration whose automorphism group is isomorphic t…

Let $G$ be a graph with at least three vertices, and let $H(G)$ be the graph constructed from $G$ whose vertices represent events consistent with the stabilizer group of the graph…

A measurement scenario consists of a set of measurements together with a family of contexts, and a probabilistic empirical model assigns compatible probability distributions to the…