From Analytic Structure to Quantum Complexity: Walsh-Pauli Representations of Continuum Operators
Abstract
How does continuum operator structure appear in a finite qubit register? We address this question for analytic functions of diagonal operators represented in a binary basis, focusing on the Jordan--Lee--Preskill (JLP) momentum operator, by developing an operator-level generating-function framework for their Walsh-Pauli spectra. The construction determines the spectrum analytically and reveals exact support and parity selection rules, together with a nontrivial intra-shell hierarchy induced by the binary encoding. This provides a systematic characterization of Walsh compressibility and its relation to Pauli locality. As a controlled application, we consider generalized uncertainty-principle (GUP) kinematics as a tunable nonlinear odd deformation of momentum, showing how higher-order momentum terms redistribute spectral weight into progressively higher Pauli-weight sectors
Related
- Commuting analytic and co-analytic Toeplitz operators on the harmonic Bergman space
- Rhaly and generalized Hilbert operators between spaces of analytic functions
- Locally analytic representations in mixed characteristic via stacks
- On the Irreducibility of Locally Analytic Vectors in Certain Banach Representations of D×
- Description Complexity Bounds for Analytic Approximations of Lipschitz Functions
BibTeX
@misc{sousa2026from,
title = {{From Analytic Structure to Quantum Complexity: Walsh-Pauli Representations of Continuum Operators}},
author = {Raphael De Sousa and Partha Nandi and Francesco Petruccione},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11350},
eprint = {2609.11350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11350},
}
RIS
TY - UNPB
TI - From Analytic Structure to Quantum Complexity: Walsh-Pauli Representations of Continuum Operators
AU - Raphael De Sousa
AU - Partha Nandi
AU - Francesco Petruccione
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11350
UR - https://arxiv.org/abs/2609.11350
AB - How does continuum operator structure appear in a finite qubit register? We address this question for analytic functions of diagonal operators represented in a binary basis, focusing on the Jordan--Lee--Preskill (JLP) momentum operator, by developing an operator-level generating-function framework for their Walsh-Pauli spectra. The construction determines the spectrum analytically and reveals exact support and parity selection rules, together with a nontrivial intra-shell hierarchy induced by the binary encoding. This provides a systematic characterization of Walsh compressibility and its relation to Pauli locality. As a controlled application, we consider generalized uncertainty-principle (GUP) kinematics as a tunable nonlinear odd deformation of momentum, showing how higher-order momentum terms redistribute spectral weight into progressively higher Pauli-weight sectors
ER -