Limits and consequesnces of nonlocality distillation
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2012
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Abstract
Only in the last few decades have we realized how to view quantum nonlocal correlations as possible information theoretic resources rather than as apparent paradoxes. Unfortunately, the past perspective in terms of paradoxes still persists in our considerations of nonlocal boxes (NLBs) that offer stronger than quantum nonlocal correlations. We argue that a more pragmatic approach is to consider the physical framework under which such correlations may be realized. Our consideration immediately yields fruit by allowing us to identify limitations of the NLB model and develop the generalized notion of a quantum nonlocal box (qNLB).
We analyze the NLB and qNLB models within the framework of nonlocality distillation protocols. The ability to concentrate the correlations of many identical noisy copies of a nonlocal correlation source is known as nonlocality distillation. The idea is still in its early stages of development and and we pursue it in this thesis. We develop multiple new nonlocality distillation protocols and prove the optimality of non-adaptive distillation protocols for both NLBs and qNLBs. We show that qNLBs offer stronger non-adaptive distillation protocols than NLBs. At the same time, the understanding we develop is that there is no single optimal adaptive protocol for N LB distillation. The choice of which protocol to use depends on the noise parameters for the NLB.
Through our investigation of nonlocality distillation protocols we conclude that the qNLB model is a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the N LB 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 limit nonlocal correlations under the framework of qNLBs rather than NLBs. As a first step towards the re-examination of such principles, we provide numerical evidence that the distillability of nonlocal correlations depends on properties that are local. We claim that the differing strength of distillation protocols for NLBs and qNLBs can be interpreted as a separation between classical and quantum predictions at the macroscopic level. This implies that there exist quantum correlations that can be observed in principle, at the macroscopic level or that the principle of macroscopic locality identifies exactly the set of quantum correlations.
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Bibliography: p. 93-106
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Citation
Rashid, J. (2012). Limits and consequesnces of nonlocality distillation (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/4738