Environment-aware transverse transport geometry for non-Gaussian oscillator states
Abstract
Non-Gaussian oscillator states are highly sensitive to weak perturbations, but reversible phase rotations and irreversible environmental changes should not be weighted equally. We introduce a finite-dimensional, direction-dependent local transport cost on a truncated Fock space and quotient it by Hamiltonian tangent directions. The resulting transverse quantity is a seminorm, not a global distance. A weighted operator frame specifies the representation cost of physical fluxes. Although the frame ({a_M,a_M^\dagger}) already spans the full trace-zero sector, multiphoton and diagonal directions can represent selected Lindblad tangents much more efficiently. Numerical tests on compass-like states show that phase rotations are removed, dephasing becomes inexpensive only after diagonal directions are included, and two- and three-photon processes are naturally captured by multiphoton frames. Thermal weights satisfy an operator-modular covariance but do not define a complete KMS geometry. The construction is therefore an environment-aware local diagnostic with explicit cutoff, regularization, and normalization conventions.
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BibTeX
@misc{coatanhay2026environmentaware,
title = {{Environment-aware transverse transport geometry for non-Gaussian oscillator states}},
author = {Arnaud Coatanhay and Angelique Dremeau},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19026},
eprint = {2609.19026},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19026},
}
RIS
TY - UNPB
TI - Environment-aware transverse transport geometry for non-Gaussian oscillator states
AU - Arnaud Coatanhay
AU - Angelique Dremeau
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.19026
UR - https://arxiv.org/abs/2609.19026
AB - Non-Gaussian oscillator states are highly sensitive to weak perturbations, but reversible phase rotations and irreversible environmental changes should not be weighted equally. We introduce a finite-dimensional, direction-dependent local transport cost on a truncated Fock space and quotient it by Hamiltonian tangent directions. The resulting transverse quantity is a seminorm, not a global distance. A weighted operator frame specifies the representation cost of physical fluxes. Although the frame ({a_M,a_M^\dagger}) already spans the full trace-zero sector, multiphoton and diagonal directions can represent selected Lindblad tangents much more efficiently. Numerical tests on compass-like states show that phase rotations are removed, dephasing becomes inexpensive only after diagonal directions are included, and two- and three-photon processes are naturally captured by multiphoton frames. Thermal weights satisfy an operator-modular covariance but do not define a complete KMS geometry. The construction is therefore an environment-aware local diagnostic with explicit cutoff, regularization, and normalization conventions.
ER -