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Doctoral thesis

No-signalling attacks and implications for (quantum) nonlocality distillation

    26.05.2015

118 p

Thèse de doctorat: Università della Svizzera italiana, 2015

Quantum key distribution
Relativistic key distribution
Nonlocality
No-signalling theories
Foundations of quantum theory
Foundations of cryptography
Device-independent key distribution
English The phenomenon of nonlocality, which can arise when entangled quantum systems are suitably measured, is perhaps one of the most puzzling features of quantum theory to the philosophical mind. It implies that these measurement statistics cannot be explained by hidden variables, as requested by Einstein, and it thus suggests that our universe may not be, in principle, a well-determined entity where the uncertainty we perceive in physical observations stems only from our lack of knowledge of the whole. Besides its philosophical impact, nonlocality is also a resource for information- theoretic tasks since it implies secrecy: If nonlocality limits the predictive power that any hidden variable (in the universe) can have about some observations, then it limits in particular the predictive power of a hidden variable held by an adversary in a cryptographic scenario. We investigate whether nonlocality alone can empower two parties to perform unconditionally secure communication in a feasible manner when only a provably minimal set of assumptions are made for such a task to be possible — independently of the validity of any physical theory (such as quantum theory). Nonlocality has also been of interest in the study of foundations of quantum theory and the principles that stand beyond its mathematical formalism. In an attempt to single out quantum theory within a broader set of theories, the study of nonlocality may help to point out intuitive principles that distinguish it from the rest. In theories where the limits by which quantum theory constrains the strength of nonlocality are surpassed, many “principles” on which an information theorist would rely on are shattered — one example is the hierarchy of communication complexity as the latter becomes completely trivial once a certain degree of nonlocality is overstepped. In order to study the structure of such super-quantum theories — beyond their aforementioned secrecy aspects — we investigate the phenomenon of distillation of nonlocality, the ability to distill stronger forms of nonlocality from weaker ones. By exploiting the inherent connection between nonlocality and secrecy, we provide a novel way of deriving bounds on nonlocality-distillation protocols through an ad
versarial view to the problem.
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https://n2t.net/ark:/12658/srd1318433
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