It was recently revealed by Cabello in a theoretical Letter [Phys. Rev. Lett. 127, 070401 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.070401] that nonlocality and contextuality, as two intuitively distinctive yet both critical quantum resources, can be surprisingly connected through Bell inequalities associated with state-independent contextuality sets. It provides a general unified method capable of converting contextuality into bipartite nonlocality. However, experimental tests of the inequalities are challenging and noise sensitive, and the requirements for the quantum states purity, dimensionality, and degree of entanglement have blocked the experimental implementation. We report a first experimental test of Cabello's inequalities from state-independent contextuality sets, by leveraging two-photon high-dimensional orbital angular momentum entangled states. Distinguishing from the standard single-particle ways, our experiment spotlights that the state-independent contextuality sets can be tested in a bipartite scenario, by which the "compatibility" or "sharpness" loopholes can be effectively avoided. Our results provide a new perspective and demonstrate the principle that contextuality, a widely used quantum resource, can be used in different physical scenarios.
The strength of quantum contextuality is closely related to quantum computation power. Yu-Oh set is the minimal quantum system with state-independent contextuality(SIC). However, its strength of the contextuality has not been taken into account. In this paper, we present a general method to determine whether there is a quantum state with strong contextuality in the quantum system composed of rank-one projectors. Based on this method, we conclude that Yu-Oh set does not have quantum states with strong contextuality. This indicates that strong contextuality and SIC are mutually independent.
We ask whether Kochen-Specker contextuality is Lorentz invariant. On the full Hilbert space, it is, since boosts act unitarily. Restricted to spin, it is not: momentum acts as an environment applying momentum-dependent Wigner rotations, leaving spin observables unsharp and breaking the operator identities behind state-independent contextuality. For spin
1/2 one scalar governs the loss, the packet average
Δ of
sin2(θW/2) (where
θW is the Wigner angle); for any spin, a ray degrades at a rate set by its spin variance transverse to the boost. In the spin-only account, the Free Will Theorem's SPIN axiom fails for every
Δ>0; the Yu-Oh set loses contextuality between
Δ≈0.008 and
0.016, with state independence going first; the Peres-Mermin square loses contextuality at
Δ≈0.059 or
0.074 by orientation; singlet CHSH loses nonlocality for
Δ≥0.159; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at
Δ≈0.206. A
q-plate implements the channel exactly on photon polarisation, with a retardation in place of the rapidity, so the nonlocality, GHZ and aimed-source results are testable without motion.
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≥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=O(n) vs
N=2Ω(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
O(n).