Quantum contextuality is a vital non-classical resource, yet illuminating the precise mechanisms through which it enables unconditional computational advantages remains a challenge. We translate graph-theoretic formulations of contextuality into an unconditional quantum memory advantage for formal language recognition. We define a promise problem on an exclusivity graph $G$ where any classical finite automaton respecting exclusivity requires $N \ge χ(G)$ memory states, whereas a QFA requires a memory of dimension $d = ξ(G)$ . The gap between these bounds isolates a structural, information-theoretic incompatibility between classical and quantum descriptions that we term \textit{representational contextuality}. For Boolean orthogonality graphs, this exacts an exponential classical memory penalty ( $d=\mathcal{O}(n)$ vs $N=2^{Ω(n)}$ ). Finally, we demonstrate a sharp algorithmic phase transition: allowing the classical machine a finite confusability of mutually exclusive events reduces this exponential classical memory cost to $\mathcal{O}(n)$ .Quantum contextuality is a vital non-classical resource, yet illuminating the precise mechanisms through which it enables unconditional computational advantages remains a challenge. We translate graph-theoretic formulations of contextuality into an unconditional quantum memory advantage for formal language recognition. We define a promise problem on an exclusivity graph $G$ where any classical finite automaton respecting exclusivity requires $N \ge χ(G)$ memory states, whereas a QFA requires a memory of dimension $d = ξ(G)$. The gap between these bounds isolates a structural, information-theoretic incompatibility between classical and quantum descriptions that we term \textit{representational contextuality}. For Boolean orthogonality graphs, this exacts an exponential classical memory penalty ($d=\mathcal{O}(n)$ vs $N=2^{Ω(n)}$). Finally, we demonstrate a sharp algorithmic phase transition: allowing the classical machine a finite confusability of mutually exclusive events reduces this exponential classical memory cost to $\mathcal{O}(n)$.

quant-pharXiv:2607.00507Jul 2, 20260 citations

Contextuality in Tree-Like Graphs

Alexei A. Strakhov, Vladimir I. Man’ko

arXiv:1404.6552Journal of Russian Laser ResearchNov 1, 20141 citation

Contextuality: The Compatibility-Hypergraph Approach

Bárbara Amaral, Marcelo Terra Cunha

SpringerBriefs in mathematicsJan 1, 20182 citations

Uniqueness of all fundamental noncontextuality inequalities

Kishor Bharti, Atul Singh Arora, L. C. Kwek +1 more

Contextuality is one way of capturing the nonclassicality of quantum theory.The contextual nature of a theory is often witnessed via the violation of noncontextuality inequalities-certain linear inequalities involving probabilities of measurement events.Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [Cabello et al.Phys. Rev. A 88, 032104 (2013); Chudnovsky et al.Ann. Math. 164, 51 (2006)] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anticyclically exclusive.Thus, the noncontextuality inequalities the underlying exclusivity structure of which is as stated, either cyclic or anticyclic, are fundamental to quantum theory.We show that there is a unique noncontextuality inequality for each nontrivial cycle and anticycle.In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing.Contextuality is one way of capturing the nonclassicality of quantum theory.The contextual nature of a theory is often witnessed via the violation of noncontextuality inequalities-certain linear inequalities involving probabilities of measurement events.Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [Cabello et al.Phys. Rev. A 88, 032104 (2013); Chudnovsky et al.Ann. Math. 164, 51 (2006)] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anticyclically exclusive.Thus, the noncontextuality inequalities the underlying exclusivity structure of which is as stated, either cyclic or anticyclic, are fundamental to quantum theory.We show that there is a unique noncontextuality inequality for each nontrivial cycle and anticycle.In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing.

arXiv:1811.05294Physical Review ResearchJul 2, 20200 citations

Measures of contextuality

Andrzej Grudka, Karol Horodecki, Michał Horodecki +5 more

Sep 17, 20120 citations

G

where any classical finite automaton respecting exclusivity requires

N \ge χ(G)

memory states, whereas a QFA requires a memory of dimension

d = ξ(G)

. The gap between these bounds isolates a structural, information-theoretic incompatibility between classical and quantum descriptions that we term \textit{representational contextuality}. For Boolean orthogonality graphs, this exacts an exponential classical memory penalty (

d=\mathcal{O}(n)

N=2^{Ω(n)}

). Finally, we demonstrate a sharp algorithmic phase transition: allowing the classical machine a finite confusability of mutually exclusive events reduces this exponential classical memory cost to

\mathcal{O}(n)