bibkey: appleby2005symmetric authors: D. M. Appleby year: 2005 title: ‘Symmetric Informationally Complete-Positive Operator Valued Measures and the Extended Clifford Group’ doi: 10.1063/1.1896384 claim: The published abstract defines the extended Clifford group as the normalizer of the generalized Pauli group, also called the Weyl-Heisenberg group; this note does not claim that the unread full text states the repository’s composition identity. strata_touched:

• D5/S3/Quantum/Algebra/WeylDisplacement license: citation-only triage: anchor

Extended Clifford Group and the Weyl-Heisenberg Displacement Words

The article is the standard modern reference for the finite-dimensional generalized Pauli group, which it also names the Weyl-Heisenberg group, and for the group of unitary and antiunitary operators normalizing it. The repository cites it to record that displacement words built from a clock and a shift are long-established objects, so no novelty is claimed for the composition phase proved in D5/S3/Quantum/Algebra/WeylDisplacement.

What was verified for this note is bibliographic identity only: author, year, journal, volume, article number, and digital object identifier, together with the published abstract naming the generalized Pauli or Weyl-Heisenberg group. The full text was not read, so this note does not assert that the article states the composition identity in the repository’s normalization, nor that it uses the same index conventions.

The pinned Mathlib source contains no Weyl-Heisenberg material at all: no file mentions the Weyl-Heisenberg group, the generalized Pauli group, or clock and shift matrices, and no file carries Pauli or Heisenberg in its name. The clock and shift generators, their Weyl relation, their orders, and their unitarity are already frozen in D5/S3/Observer/WindowRegister, which the displacement module imports rather than reproves.