Quantum Nonlocal Boxes Exhibit Stronger Distillability

TL;DR

This paper demonstrates that quantum nonlocal boxes ( extsf{qNLB}s) can be distilled into stronger correlations than classical nonlocal boxes ( extsf{NLB}s), challenging the notion that extsf{NLB}s are the ultimate resource for nonlocality.

Contribution

The authors introduce a new distillation protocol for extsf{qNLB}s, showing they are a stronger resource for nonlocality than extsf{NLB}s, and argue for reconsidering fundamental principles of quantum nonlocality.

Findings

extsf{qNLB}s can be asymptotically distilled to a higher nonlocal value than classical extsf{NLB}s.

The proposed protocol is optimal for 1, 2, and 3 extsf{qNLB} copies.

extsf{qNLB}s challenge the current understanding of nonlocality limitations.

Abstract

The hypothetical nonlocal box (\textsf{NLB}) proposed by Popescu and Rohrlich allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the \textsf{NLB}. Motivated by the limited distillability of \textsf{NLB}s, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (\textsf{qNLB}s). We propose a new protocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value $1/2 (3\sqrt{3}+1) \approx 3.098076$, whereas in contrast, the optimal non-adaptive parity protocol for classical nonlocal boxes asymptotically distills only to the value 3.0. We show that our protocol is an optimal non-adaptive protocol for 1, 2 and 3 \textsf{qNLB} copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that \textsf{qNLB}s are a stronger resource for nonlocality than \textsf{NLB}s. The main premise that develops from this conclusion is that the \textsf{NLB} model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that are known to limit nonlocal correlations under the framework of \textsf{qNLB}s rather than \textsf{NLB}s.