Step 1: Understanding non-cyclic photophosphorylation.
Non-cyclic photophosphorylation involves both Photosystem II and Photosystem I and results in the formation of ATP, NADPH, and oxygen.
Step 2: Conditions required for the process.
This process requires the presence of oxygen-releasing reactions, sufficient light intensity to excite both photosystems, and high CO$_2$ concentration to support subsequent carbon fixation.
Step 3: Analysis of options.
Options (A), (B), and (D) do not satisfy all the essential conditions required for non-cyclic photophosphorylation. Option (C) correctly mentions aerobic conditions, high CO$_2$ concentration, and enough light intensity.
Step 4: Conclusion.
Thus, the correct answer is (C) aerobic conditions, high CO$_2$ concentration and enough light intensity.