  In classical physics, a single measurement can in principle reveal the state
of a system. However, quantum theory permits numerous non-equivalent
measurements on a physical system, each providing only limited information
about the state. This set of various measurements on a quantum system indicates
a rich internal structure. We illuminate this structure for both individual and
composite systems by conceptualizing measurements as questions with a finite
number of outcomes. We create a mathematical question structure to explore the
underlying properties, employing the concept of information as a key tool
representing our knowledge gained from asking these questions. We subsequently
propose informational assumptions based on properties observed from
measurements on qubits, generalizing these to higher dimensional systems.
  Our informational assumptions shape the correlations between subsystems,
which are symbolized as classical logical gates. Interestingly, systems with
prime number dimensions exhibit unique property: the logical gate can be
expressed simply as a linear equation under modular arithmetic. We also
identify structures in quantum theory that correspond to those in the structure
of quantum questions. For instance, the questions determining the system
correspond to generalized Pauli matrices, and the logical gate connecting
questions in subsystems is directly related to the tensor product combining
operators. Based on these correspondences, we present two equivalent scenarios
regarding the evolution of systems and the change of information within both
quantum questions and quantum mechanics.
