Bell monogamy

Abstract

A single Bell's inequality is violated by quantum predictions and demonstrates impossibility of classical-like model beyond quantum statistics. Interestingly, several Bell inequalities often cannot be violated simultaneously--a fact known as Bell monogamy. In this thesis we will formulate a method within graph theory to obtain the Bell monogamy relations from no-signalling principle. We also borrowed the derivation used to obtain the entropic uncertainty relation to re-derive the bound on Bell monogamy relation using the correlation complementarity principle. It is shown that a tighter bound could in principle be obtained using this new derivation. We introduce the notion of elementary monogamy relations and solve completely their existence for bipartite Bell inequalities. We obtain three elementary tripartite Bell monogamy relations from the complementarity principle and we conjecture that there is no finite set of elementary Bell monogamy relations in the multipartite case.