Graph-theoretic Approach To Contextuality Of Three-qubit Hypergraph States

Hypergraph states are considered to be a special case of the local maximum entangled states and have also been shown to violate locality in a way exponentially growing with the number of particles.In addition,hypergraph states exist in some quantum algorithms such as the Deutsch-Jozsa algorithm and the Grover algorithm.Hypergraph states can be a fine test platform for exploring the subtleties of multi-particle entanglement.Quantum contextuality,meaning that the measurement of a quantum state may depend on other compatible measurements performed on this system,is an important research direction in the field of quantum computing.Under the measurement-based quantum computations,computing nonlinear Boolean functions with high probability is contextual.The calculation of this kind of context property has super-polynomial level acceleration than the classical algorithm's,and this advantage can solve the discrete logs problems.Furthermore,quantum contextuality is a critical resource for finding quantum states suitable for the magic state distillation(MSD)protocol.Cabello-Severini-Winter(CSW)and Abramsky-Hardy use different mathematical techniques to provide some methods for calculating contextual inequalities for common experimental scenarios.Gühne et al.proved that fully connected k-uniform hypergraph states can generate non-contextuality inequalities by imitating the GHZ theory.Gachechiladze et al.translated Hardy-type arguments into Bell inequalities,and proved that the violation of N-bit three-uniform hypergraph states increase exponentially with the number of particles.In this paper,we mainly study the contextuality of each of the three-qubit hypergraph states as following two parts:(1)we utilize the graph-theoretic framework proposed to characterize correlations between noncontextual theories and the quantum theory by CSW,to emerge the noncontextuality inequalities of the three-qubit hypergraph states,and prove that all the three-qubit hypergraph states with a single hyperedge allow for the contextuality.(2)we generate our approach to the three-qubit ordinary graph states by the stabilizer operator,such as GHZ state and the common graph states.So far,we explore the contextuality of all the three-qubits hypergraph states and prove that all of them allow for this kind of contextuality.This paper provides a navel approach for studying the contextuality of the hypergraph states.Finally,the improvement of this paper and the prospect of future work are putting forward.