Non-locality and entanglement in multi-qubit systems from a unified framework

Non-classical probability is the underlying feature of quantum mechanics. The emergence Bell-CHSH non-locality [We stress that CHSH inequality (Clauser et al. in Phys. Rev. Lett. 23(15):880, 1969) more general and reduces to Bell (Bell Physics 1:195, 1964) under assumption perfect correlations between observables] for bipartite systems linear entanglement inequalities two-qubit has been shown Adhikary (Eur Phys J D 74:68, 2020), purely as violations classical rules. In this paper, we improve upon work by showing violation any nonlocality implies rules, manifested through negative probabilities, without recourse theory. Moving on entanglement, employ parent pseudoprojections show how number nonlinear witnesses multiqubit can be obtained They include ones have derived earlier employing different methods. It provides a perspective complementary current understanding terms algebraic approaches.