Generalized nonlocality criteria under the correlation symmetry

Abstract

The most general class of non-locality criteria for N -partite d-chotomic systems with k number of measurement settings is derived under the constraint of measurement symmetries. It is the complete characterisation of the multi-partite non-locality when the correlation is assumed to be symmetric under the choice of measurement settings. The generalized non-locality condition is obtained using the correlation functions, which are derived from Fourier analysis of probability spectrums. It is found that the condition for the local hidden variable (LHV) model is violated by multipartite quantum states and general constraints for the quantum violation of maximally entangled state has been obtained.

Bell-Type Correlation at Quantum Phase Transitions in Spin-1 Chain

“…Our description is made not by a set of probabilities but by the form of correlation functions. It can be proved that the representations are equivalent as long as an appropriate collection of the correlations is made through the right choices of weighting coefficients [ 21 ].…”

“…Based upon this expression, CGLMP correlation can be described by the expectation value of the following composite operator, when the weight function becomes . As addressed in [ 21 ], the weight can be specified for the convex sum of the probability distributions suggested by Collins et al [ 19 ]. Bell correlation Equation (4) for the case of is obviously equivalent to one in the CHSH inequality.…”

“…Bell correlation Equation (4) for the case of is obviously equivalent to one in the CHSH inequality. The local realistic bounds of the CGLMP correlation for are given by , which can be derived from [ 21 ].…”

“…In other words, Bell correlations in d -dimensional systems of many particles have been rarely investigated, whereas the other measures of quantum information theory, such as fidelity and quantum coherence, are used to characterize the quantum phase transitions (QPTs) many times in spin-1 chains or more [ 16 , 17 , 18 ]. In this work, we use a generalized high-order Bell correlation obtained from high-dimensional spin measurements, which is proposed by D. Collins et al [ 19 ] and W. Son et al [ 20 , 21 ]. Then, we analyze its Bell correlation in the spin-1 chain to identify diverse quantum phase transitions.…”

Noise resistance of activation of the violation of the Svetlichny inequality

“…Nonlocality is one of the most fundamental properties of quantum theory. In recent years, nonlocal correlations were found to be useful in many applications in quantum information theory; see, e.g., [3,5,6,[9][10][11]13,21,24]. Initially, nonlocality was considered in a bipartite case.…”