Quantum complementarity through entropic certainty principles

We approach the physical implications of non-commutative nature Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that sum two relative entropies, naturally related to COA, is equal so-called algebraic index associated inclusion. Uncertainty relations then arise by monotonicity entropies participate in underlying entropic certainty. Examples and applications are described quantum field theories with global symmetries, where COA formed charge-anticharge local operators (intertwiners) unitary representations symmetry group (twists), Wilson 't Hooft loops. general, principle captures physics order/disorder parameters, feature makes it generic handle for characterization phases.