Figure 2.

Bivariate decomposition of $I(123;12)$ for the XOR system. (A) Joint distribution of the inputs 1 and 2 and the output 3 for the XOR operation. We also collect the value of the information-theoretic quantities used to calculate this bivariate decomposition and the trivariate decomposition $I(123;123)$ in Section 5.2. (B) Bivariate decomposition derived from the weak stochasticity axiom. Stochastic and deterministic components are separated in agreement with Table 1. (C) Bivariate decomposition derived from the strong axiom. Only deterministic components are present, following Table 2.