Classical and Quantum MacWilliams Transforms as Spin Kinematics

Abstract:Spin is the hidden engine behind the zoo of MacWilliams transforms in weight enumerator theories - not only for qubits and qudits, but even for classical codes. From nothing more than a split into trivial and nontrivial errors, we kinematically derive the MacWilliams transform as a Wigner-$D$ rotation between two canonical bases. Within each classical and quantum theory, changing the length $n$ leaves the rotation untouched: the same element simply reappears at spin $n/2$. And at fixed $n$, changing the rotation axis simply moves between the various classical and quantum theories.

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2607.27173 [quant-ph]

(or arXiv:2607.27173v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.27173 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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