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

TL;DR

This paper proves that within the 2x2 case, operations transforming local boxes into local ones cannot broadcast nonlocal boxes, using a property called anti-Robustness that cannot decrease under such operations.

Contribution

It establishes a no-broadcasting theorem for non-signalling boxes under a specific class of local-preserving operations, introducing anti-Robustness as a key tool.

Findings

Broadcasting of nonlocal boxes is impossible in 2x2 case.

Anti-Robustness cannot decrease under local-preserving operations.

The proof reduces to showing anti-Robustness would decrease after broadcasting.

Abstract

We deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class can not broadcast a nonlocal box in 2x2 case. We consider a function called anti-Robustness which can not decrease under these operations. The proof reduces to showing that anti-Robustness would decrease after broadcasting.