Cubic blindness and quartic recovery in scalar Rains invariants of four-qubit rank-two code projectors
Scalar Rains invariants of degree k are k-copy observables for quantum-code projectors, yet the copy order required for local differential separation is poorly understood. We construct an explicit eight-dimensional family of rank-two four-qubit code projectors whose complete degree-at-most-three transcript has rank seven on a smooth five-dimensional critical germ. On a skew-Hermitian sheet, every quadratic and cubic coordinate reduces to three pair purities. The unique blind tangent is non-local-unitary and changes only the determinant of a Bell-diagonal marginal. A connected crossed quartic realignment moment supplies the missing cotangent direction and restores rank eight, establishing an exact four-copy local threshold. This is a preprint and has not yet undergone journal peer review.
Authors
- Samuele Garbati (ORCID: https://orcid.org/0009-0002-0784-6167)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-07-24
- DOI
- https://doi.org/10.5281/zenodo.21530434
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- preprint