Bell inequalities for continuous-variable correlations.
We derive a new class of correlation Bell-type inequalities. The inequalities are valid for any number of outcomes of two observables per each of n parties, including continuous and unbounded observables. We show that there are no first-moment correlation Bell inequalities for that scenario, but such inequalities can be found if one considers at least second moments. The derivation stems from a simple variance inequality by setting local commutators to zero. We show that above a constant detector efficiency threshold, the continuous-variable Bell violation can survive even in the macroscopic limit of large n. This method can be used to derive other well-known Bell inequalities, shedding new light on the importance of non-commutativity for violations of local realism.
Cavalcanti
E G
EG
ARC Centre of Excellence for Quantum-Atom Optics, The University of Queensland, Brisbane, Australia.
Foster
C J
CJ
Reid
M D
MD
Drummond
P D
PD