Generalized n‐Locality Inequalities in Linear‐Chain Network for Arbitrary Inputs Scenario and Their Quantum Violations

Multipartite nonlocality in a network is conceptually different from standard multipartite Bell nonlocality. In recent times, network nonlocality has been studied for various topologies. A linear‐chain topology of the network is considered and the quantum nonlocality (the non‐n‐locality) is demonstrated. Such a network scenario involves n number of independent sources and n+1$n+1$ parties, two edge parties (Alice and Charlie), and n−1$n-1$ central parties (Bobs). It is commonly assumed that each party receives only two inputs. In this work, a generalized scenario where the edge parties receive an arbitrary n number of inputs (equals to a number of independent sources) is considered and each of the central parties receives two inputs. A family of generalized n‐locality inequalities for a linear‐chain network for arbitrary n is derived and the optimal quantum violation of the inequalities is demonstrated. An elegant sum‐of‐squares approach enabling the derivation of the optimal quantum violation of aforesaid inequalities without assuming the dimension of the system is introduced. It is shown that the optimal quantum violation requires the observables of edge parties to be mutually anticommuting. Nonlocality in linear‐chain network featuring two edge parties and arbitrary number of central parties (Bobs) is demonstrated. A family of generalized n‐locality inequalities where edge parties receive arbitrary inputs and each central party receives two inputs is proposed. Optimal quantum violations of the inequalities to demonstrate network nonlocality are derived.