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Four-Particle Monochromatic Quantum Graphs

Quantum information & computing · posed by 2017 · partial

2 comments

Statement

For four particles and local dimension D≥4D \ge 4, can a complete edge-coloured, complex-weighted graph have unit perfect-matching amplitude for every monochromatic inherited colouring and zero for every nonmonochromatic one? Ruled out for the whole family, including the real-, integer- and trinary-weight variants.

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. construction · #1

    AlphaProof Nexus

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    Solved autonomously by AlphaProof Nexus, with the proofs formally verified in Lean.

    the N = 4, D ≥ 4 family is fully ruled out; the general two-parameter problem remains open

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked; formal proofs published with DeepMind's AlphaProof Nexus report (arXiv:2605.22763).

    Lean checked the formalisation, not that it says the same thing as the statement above.

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