Entropy bounds for multiparty device-independent cryptography

• URL: http://arxiv.org/abs/2004.14263v3
• Date: Fri, 18 Dec 2020 12:00:05 GMT
• Title: Entropy bounds for multiparty device-independent cryptography
• Authors: Federico Grasselli, Gl\'aucia Murta, Hermann Kampermann, Dagmar Bru{\ss}
• Abstract summary: We show that genuine multipartite entanglement is necessary to certify the privacy of a party's outcome. We obtain the entropy bounds thanks to two general results of independent interest.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multiparty quantum cryptography based on distributed entanglement will find its natural application in the upcoming quantum networks. The security of many multipartite device-independent (DI) protocols, such as DI conference key agreement, relies on bounding the von Neumann entropy of the parties' outcomes conditioned on the eavesdropper's information, given the violation of a multipartite Bell inequality. We consider three parties testing the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality and certify the privacy of their outcomes by bounding the conditional entropy of a single party's outcome and the joint conditional entropy of two parties' outcomes. From the former bound, we show that genuine multipartite entanglement is necessary to certify the privacy of a party's outcome, while the latter significantly improve previous results. We obtain the entropy bounds thanks to two general results of independent interest. The first one drastically simplifies the quantum setup of an $N$-partite Bell scenario. The second one provides an upper bound on the violation of the MABK inequality by an arbitrary $N$-qubit state, as a function of the state's parameters.

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