Pointer States Are Not Enough: Physical Monitor Selection in a Finite Quantum Register

Abstract

A candidate pointer basis, an algebra generated by available microscopic operations, and the pointer structure of a physically selected open-system channel are different objects. We exhibit that distinction in an exact eight-qubit register. The qubits occupy the eight triangular faces of a bond-centred oblate square bipyramid; their adjacency graph is the cube graph Q₃. Twelve commuting edge-parity observables have rank seven and therefore leave 128 two-dimensional complement sectors. On the 48 valid register labels these become eight rank-two sectors and 32 rank-one sectors. The result for service operations depends on which records are physically exported. Under full polarity-resolved J/K support, eight of the 24 pairs differing only in I₃ are distinguished directly, eight by composition, and eight survive; 32 of 48 labels are individuated. Under the banked elementary positive-branch event, J alone individuates only 22 of 48, with residual multiplicity in all three generations. Nevertheless the generation-00 noiseless factor is support-robust: on the same fixed 48-state closure, both algebras satisfy A_JK|O₀₀ ≅ B_JK ⊗ I_{I₃} and A_J|O₀₀ ≅ B_J ⊗ I_{I₃}, with support-dependent quotient algebras. A further exact no-go sharpens the physical boundary. Coherent evolution, an address-only L record and polarity-resolved J/K records can share the same 224 exit edges while preserving different coherences and generating different resolving algebras. Only polarity-resolved export gives the conditional finite hierarchy 01 < 10 < 00; executing the missing edges is not enough. The remaining task is therefore not simply to choose rates, but to derive a polarity-complete schedule, retain its fired-arm flag, export that flag to a fresh orthogonal environment record and license branchwise recovery. Three interference/rate experiments distinguish these clauses exactly.

Keywords

How to cite

Elliman, D. (2026). Pointer States Are Not Enough: Physical Monitor Selection in a Finite Quantum Register. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.22003393

@techreport{elliman2026pointerstatesnotenough,
  author      = {Elliman, David},
  title       = {Pointer States Are Not Enough: Physical Monitor Selection in a Finite Quantum Register},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.22003393},
  url         = {https://neusym.ai/papers/pointer_states_not_enough/}
}