Entanglement allows for the nonlocality of quantum theory, which is the
resource behind device-independent quantum information protocols. However, not
all entangled quantum states display nonlocality, and a central question is to
determine the precise relation between entanglement and nonlocality. Here we
present the first general test to decide whether a quantum state is local, and
that can be implemented by semidefinite programming. This method can be applied
to any given state and for the construction of new examples of states with
local hidden-variable models for both projective and general measurements. As
applications we provide a lower bound estimate of the fraction of two-qubit
local entangled states and present new explicit examples of such states,
including those which arise from physical noise models, Bell-diagonal states,
and noisy GHZ and W states.Comment: Published version with new title and abstract, improved presentation
and new examples of LHV states. Codes are available at
https://github.com/paulskrzypczyk/localhiddenstatemodels (please cite this
paper if you use them). See also the related work by F. Hirsch et al
arXiv:1512.0026
