14 problems

For odd-prime-dimensional qudits, the Wigner polytope is the set of states with non-negative discrete Wigner function; a pure magic state is a pure non-stabilizer state usable as a…

Contextuality is a property of quantum states manifested through measurements whose outcomes cannot be explained by a noncontextual hidden-variable model. Universal quantum computa…

Dzhafarov–Kujala proportionality conjecture. In the class of cyclic systems, $\text{CNT}_{3}$ and $\text{CNT}_{2}$ should be proportional.

A cyclic system is a collection of binary random variables arranged in a cycle, and let $\text{CNT}_{1}$, $\text{CNT}_{2}$, and $\text{CNT}_{3}$ denote the contextuality measures u…

Let a contextuality model be evaluated in the hierarchy of $n$-contextuality, where increasing $n$ permits inclusion of larger simplices in the underlying simplicial complex, and l…

Quotient conjecture. The passage from $S$ to $\tuple{S,g}$ might correspond to taking quotients of (generalized) partial Boolean algebras.

State-extension conjecture. If state $\nu$ of $A$ satisfies PEP, then there is a state $\hat{\nu}$ of $A[\perp]$ such that

LEP--PEP converse conjecture. If PEP holds, then LEP holds:

Fixpoint conjecture. $A[\perp]^*$ coincides with iterating $A[\perp]$ to a fixpoint.

The invariant partial ideal conjecture. A partial ideal of $\mathcal{A}$ arises from a total ideal if and only if it is an invariant partial ideal. Consequently, the map…

Let $V_i$) and $W_i$ ($i=1,\dots,n$) be $\pm1$-valued random variables arranged in a cyclic system, with $W_{i\oplus1}$ paired with $V_i$. Write $\langle\cdot\rangle$ for expectati…

Let $H_1,\ldots,H_n$ be contextuality scenarios, let $\overline{H_1\otimes\ldots\otimes H_n}$ denote the completion of their $n$-fold product scenario, let $\bar H_i$ denote the co…

Let $H$ be a contextuality scenario and let $C^*(H)$ denote its universal unital $C^*$-algebra. The decision problem $\mathtt{ALLOWS\_QUANTUM}$ asks whether a given contextuality s…

The paper distinguishes two notions of contextuality, one important in the Consistent Histories program and another associated with topos-theoretic approaches to quantum theory. Co…