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Recently, it was demonstrated by Son et al., Phys. Rev. Lett. \textbf{102},110404 (2009), that a separable bipartite continuous variable quantum systemcan violate the Clauser-Horne-Shimony-Holt (CHSH) inequality via operationallylocal transformations. Operationally local transformations are parameterizedonly by local variables, however in order to allow violation of the CHSHinequality a maximally entangled ancilla was necessary. The use of theentangled ancilla in this scheme caused the state under test to becomedependent on the measurement choice one uses to calculate the CHSH inequalitythus violating one of the assumptions used in deriving a Bell inequality,namely the `free will' or `statistical independence' assumption. The novelty inthis scheme however is that the measurement settings can be external freeparameters. In this paper we generalize these operationally localtransformations for multipartite Bell inequalities (with dichotomicobservables) and provide necessary and sufficient conditions for violationwithin this scheme. Namely, a violation of a multipartite Bell inequality inthis setting is contingent on whether an ancillary system admits any realistic,local hidden variable model i.e. whether the ancilla violates the given Bellinequality. These results indicate that violation of a Bell inequalityperformed on a system does not necessarily imply that the system is nonlocal.In fact the system under test may be completely classical. However, nonlocalitymust have resided somewhere, this may have been in the environment, thephysical variables used to manipulate the system or the detectors themselvesprovided the measurement settings are external free variables.

Violation of multipartite Bell inequalities with classical subsystems via operationally local transformations