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We propose an uncertainty-complementarity balance relation and buildquantitative connections among non-locality, complementarity, and uncertainty.Our balance relation, which is formulated in a theory-independent manner,states that for two measurements performed sequentially, the complementaritydemonstrated in the first measurement in terms of disturbance is no greaterthan the uncertainty of the first measurement. Quantum theory respects ourbalance relation, from which the Tsirelson bound can be derived, up to aninessential assumption. In the simplest Bell scenario, we show that the boundof Clauser-Horne-Shimony-Holt inequality for a general non-local theory can beexpressed as a function of the balance strength, a constance for the giventheory. As an application, we derive the balance strength as well as thenonlocal bound of Popescu-Rohrlich box. Our results shed light on quantitativeconnections among three fundamental concepts, i.e., uncertainty,complementarity and non-locality.

Uncertainty-Complementarity Balance as a General Constraint on Non-locality