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.

arXiv:2609.19026 [quant-ph]

(or arXiv:2609.19026v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.19026 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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