Intrinsic Non-Locality and Device-Independent Conference Key Agreement

Conference key agreement is a multipartite protocol that can be executed using genuinely multipartite entangled resources. Several questions remain unanswered with regards to device-independent conference key agreement rates. In this work, we introduce the multipartite intrinsic non-locality as a resource quantifier for the multipartite scenario of device-independent conference key agreement. We prove that this quantity is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for multipartite mutual information, which may be of independent interest. We then use this chain rule to establish the multipartite intrinsic non-locality as an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement. We discuss various examples of DI conference key protocols and compare our upper bounds for these protocols with known lower bounds. Upper bounds on recent experimental realizations of device-independent quantum key distributions are also calculated.