Distillation of n-GHZ Box

Xin-Wen Wang, Shi-Qing Tang, Ji-Bing Yuan +1 more

Ji-Bing Yuan, Shi-Qing Tang, Xin-Wen Wang +1 more

Guo‐Zhu Pan, Chao Li, Ming Yang +2 more

Talha Lateef

In quantum mechanics some spatially separated sub-systems behave as if they are part of a single system, the superposition of states of this single system cannot be written as products of states of individual sub-systems,we say that the state of such system is entangled, such systems give rise to non-local correlations between outcomes of measurements. The non-local correlations are conditional probability distributions of some measurement outcomes given some measurement settings and cannot be explained by shared information.These correlations can be studied using a non-local box(NLB) which can be viewed as a quantum systema. A NLB is an abstract object which has number of inputs(measurement settings) and number of outputs(outcomes), such NLBs can be both quantum and super-quantum. The correlations are of use in quantum information theory, the stronger the correlations the more useful they are, hence we study protocols that have multiple weaker non-local systems, application of these protocols to weaker systems may result in stronger non-local correlations, we call such protocols non-locality distillation protocols. In our work here we present non-locality distillation protocols for tripartite NLBs specifically GHZ box and class 44,45 and 46 of no-signalling polytope.

Peter Høyer, Jibran Rashid

The hypothetical nonlocal box (NLB) proposed by Popescu and Rohrlich allows two spatially sepa-rated 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 NLB. Motivated by the limited distillability of NLBs, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (qNLBs). We propose a new pro-tocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value 12 (3 3 + 1) ≈ 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 qNLB copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that qNLBs are a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the 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

Keng-Shuo Wu, Li‐Yi Hsu