Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities

Abstract

The phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as XOR games, and to a restricted set of unique games. In many instances of interest, we show that the derived relation provides a significant strengthening over previously known results. The result involves a shift in paradigm towards the importance in monogamies of the number of inputs of one party which lead to a contradiction from local realistic predictions.