  We develop an operational approach for reconstructing the quantum theory of
qubit systems from elementary rules on information acquisition. The focus lies
on an observer O interrogating a system S with binary questions and S's state
is taken as O's `catalogue of knowledge' about S. The mathematical tools of the
framework are simple and we attempt to highlight all underlying assumptions.
Four rules are imposed, asserting (1) a limit on the amount of information
available to O; (2) the mere existence of complementary information; (3) O's
total amount of information to be preserved in-between interrogations; and, (4)
O's `catalogue of knowledge' to change continuously in time in-between
interrogations and every consistent such evolution to be possible. This
approach permits a constructive derivation of quantum theory, elucidating how
the ensuing independence, complementarity and compatibility structure of O's
questions matches that of projective measurements in quantum theory, how
entanglement and monogamy of entanglement, non-locality and, more generally,
how the correlation structure of arbitrarily many qubits and rebits arises. The
rules yield a reversible time evolution and a quadratic measure, quantifying
O's information about S. Finally, it is shown that the four rules admit two
solutions for the simplest case of a single elementary system: the Bloch ball
and disc as state spaces for a qubit and rebit, respectively, together with
their symmetries as time evolution groups. The reconstruction for arbitrarily
many qubits is completed in a companion paper (arXiv:1511.01130) where an
additional rule eliminates the rebit case. This approach is inspired by (but
does not rely on) the relational interpretation and yields a novel formulation
of quantum theory in terms of questions.
