  The so-called preparation uncertainty can be understood in purely operational
terms. Namely, it occurs when for some pair of observables, there is no
preparation, for which they both exhibit deterministic statistics. However, the
right-hand side of uncertainty relation is generally not operational as it
depends on the quantum formalism. Also, while joint non-measurability of
observables is an operational notion, the complementarity in Bohr sense (i.e.
excess of information needed to describe the system) has not yet been expressed
in purely operational terms.
  In this paper we propose a solution to these problems, by introducing an
operational definition for complementarity, and further postulating uncertainty
as a necessary price for complementarity in physical theories. In other words,
we propose to put the (operational) complementarity as the right-hand side of
uncertainty relation.
  Concretely, we first identify two different notions of uncertainty and
complementarity for which the above principle holds in quantum mechanics. We
also introduce postulates for the general measures of uncertainty and
complementarity. In order to define quantifiers of complementarity we first
turn to the simpler notion of independence that is defined solely in terms of
statistics two observables.
  We also use our framework to define new complementarity indicators based on
(i) performance of random access codes, (ii) geometrical properties of the body
of observed statistics, and (iii) variation of information. We then show that
they can be used to state uncertainty relations. Moreover, we show that
non-signaling and uncertainty relation expressed by complementarity of type
(ii) leads to the Tsirelson bound for CHSH inequality. Lastly, we show that a
variant of Information Causality called Information Content Principle, can be
interpreted as uncertainty relation in the above sense.

Quantum Physics