Connes spectral distance and nonlocality of generalized noncommutative phase spaces

We study the Connes spectral distance of quantum states and analyse nonlocality a 4D generalized noncommutative phase space. By virtue Hilbert–Schmidt operatorial formulation, we obtain Dirac operator construct triple corresponding to Based on ball condition, some constraint relations about optimal elements, then calculate between two Fock states. Due noncommutativity, distances in spaces are shorter than those normal spaces. This shortening implies type caused by noncommutativity. These space additive satisfy Pythagoras theorem. When parameters go zero, results return