Quantum Interference Needs Convention: Overlap-Determinability and Unified No-Superposition Principle

• URL: http://arxiv.org/abs/2601.14638v1
• Date: Wed, 21 Jan 2026 04:25:21 GMT
• Title: Quantum Interference Needs Convention: Overlap-Determinability and Unified No-Superposition Principle
• Authors: Jeongho Bang, Kyoungho Cho, Ki Hyuk Yee,
• Abstract summary: Quantum superposition is often phrased as the ability to add state vectors.<n>We formalize this through phase conventions and a single notion -- dubbed as "overlap-determinability"<n>We show that granting universal access to such convention-fixed overlaps destabilizes the familiar foundational and computational constraints.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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 as "overlap-determinability." Our main theorem gives an exact equivalence: A nonzero completely positive trace-nonincreasing map that probabilistically produces superposition on a domain exists if and only if that domain is overlap-determinable. This unifies modern no-superposition results and characterizes 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 super-luminal signaling. It would also permit reflections about unknown states, leading to exponentially fast overlap amplification and a collapse of Grover's search lower bound to a logarithmic query complexity.

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