Quantum superposition is often phrased as the ability to add state vectors. In practice, however, the physical quantity is a ray (a rank-one projector), so each input specifies only a projector and leaves a gauge freedom in the phases of its vector representatives. This becomes a real operational barrier when one asks for a device that, given two independently prepared unknown pure states, outputs a coherent state proportional to a prescribed linear combination. We identify the missing ingredient as not probabilistic but phase-like. One needs a physical scenario that fixes a single phase convention on the relevant set of rays, so that the overlaps become well-defined complex numbers. Thus, we formalize this through phase conventions and a single notion—dubbed “overlap determinability.” Our main result clarifies the no-go and constructive aspects of this statement: overlap determinability is a necessary operational phase resource for generic coherent superposition, while the converse is asserted only when the phase convention is physically supplied and implementable, as in the standard reference-state promise. This reformulation unifies modern no-universal-superposition results and reinterprets the exceptional yes-go protocols, which succeed precisely when side information supplies the required missing resource. We then show that granting universal access to such convention-fixed overlaps destabilizes the familiar foundational and computational constraints. It enables forbidden transformations akin to quantum cloning and yields superluminal signaling. It also permits reflections about unknown states, leading to exponentially fast amplitude amplification and a collapse of Grover's search bound to a logarithmic query complexity.

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• Quantum foundations
• Quantum information theory