2026/07/20 by Elena R. Loubenets
#quant-ph #math-ph #math.MP
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general condition sufficient for a nonseparable Werner state with a dimension d≤min\S1,S2\ to satisfy all Bell inequalities under every S1× S2-setting correlation scenario with outcomes of an arbitrary spectral type, discrete or continuous - that is, to be S1× S2-setting Bell local, for short. For a variety of S1,S2≥1 values, this new general locality condition is beyond Werner's and Barrett's locality conditions for a nonseparable Werner state. We also prove explicitly in the operator terms the optimization result by Terhal et. el. [Phys. Rev. Lett. 90, 157903 (2003)] via semi-programming that every nonseparable Werner state with a dimension d>min\S1,S2\ is S1× S2 -setting Bell local. The new results of the present article are important both for Bell nonlocality theory and for quantum applications based on Bell nonlocality.