No-broadcasting of non-signalling boxes via operations which transform local boxes into local ones

摘要

We deal with families of probability distributions satisfying non-signallingcondition, called non-signalling boxes and consider class of operations thattransform local boxes into local ones (the one that admit LHV model). We provethat any operation from this class can not broadcast a nonlocal box in 2x2case. We consider a function called anti-Robustness which can not decreaseunder these operations. The proof reduces to showing that anti-Robustness woulddecrease after broadcasting.