Studying Coherence,bound Of Nonlocality In An Axiomatic Manner And A New Interpretation Of Quantum Complementarity

The researches of quantum non-locality help us to preclude a local realistic inter-pretation.However,quantum mechanics has many other non-classical features while they have not been well-studied in a similar manner with non-locality,such as coher-ence,and complementarity.To specify quantum mechanics from a general theory,the features and the connections among them must be studied overall in an operational man-ner.In this manuscript,we introduce an operational coherence-quantification frame-work,and propose an uncertainty-coherence balance relation.The relation is represent-ed without relying on the structure of quantum mechanics but respected by quantum mechanics.We then introduce a balance strength for a general discussion.We find that the non-local bound for a general theory is a function of the balance strength.As appli-cations,we explain the quantum non-local bound and the PR-box nonlocal bound with their balance strengths.We provide a general coherence quantification framework and give quantitative connections among three fundamental properties,namely,uncertainty complementarity and non-locality.We interpret(?)the quantum complementarity based on unbiased parameter esti-mation.We notice that the information obtained from previous measurement can be used to remove the bias it introduced to a sequential measurement.Thus,we can unbi-asedly estimate the parameters characterizing incompatible observables and study the complementarity within estimation theory.We provide new interpretations of com-plementarity relation based on estimation theory,i.e.,the trade-off between the Fisher information of parameters and the trade-off between the accuracy of incompatible mea-surements.