Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations
TL;DR: It is shown that monogamy of Bell's inequality violations, which is strictly weaker condition than the no-signaling principle is enough to prove security of quantum key distribution, and generalize the results to any theory that communicating parties may have access to.
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Abstract: We show that monogamy of Bell's inequality violations, which is strictly weaker condition than the no-signaling principle is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect the no-signaling principle yet still allow for secure communication. This proves that no signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.
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Citations
Are general quantum correlations monogamous
TL;DR: It is proved, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous.
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Monogamy of correlations versus monogamy of entanglement
TL;DR: The relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial.
Should entanglement measures be monogamous or faithful
Cécilia Lancien,Cécilia Lancien,Sara Di Martino,Marcus Huber,Marcus Huber,Marcus Huber,Marco Piani,Gerardo Adesso,Andreas Winter,Andreas Winter +9 more
TL;DR: It is shown that every additive and suitably normalized entanglement measure cannot satisfy any nontrivial general monogamy relation while at the same time faithfully capturing the geometric entangler structure of the fully antisymmetric state in arbitrary dimension.
Monogamy of entanglement of formation
TL;DR: In this article, it was shown that the entanglement of formation cannot be freely shared and therefore should be said to be monogamous, and that the squared concurrence does not obey the same relation as the concurrence.
Generalized monogamy of contextual inequalities from the no-disturbance principle.
TL;DR: It is shown how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution.
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