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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2601.14638 |
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| _version_ | 1866917214724030464 |
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| author | Bang, Jeongho Cho, Kyoungho Yee, Ki Hyuk |
| author_facet | Bang, Jeongho Cho, Kyoungho Yee, Ki Hyuk |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Interference Needs Convention: Overlap-Determinability and Unified No-Superposition Principle Bang, Jeongho Cho, Kyoungho Yee, Ki Hyuk Quantum Physics 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. |
| title | Quantum Interference Needs Convention: Overlap-Determinability and Unified No-Superposition Principle |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.14638 |