Quantum Loads and the Generalized Telegrapher's Problem
Abstract
We report on the mapping of classical microwave transmission line theory onto the quantum scattering matrix description. By means of a generalized flux formalism a la Devoret, we derive a charge-current vector living on the confining electrodes, to which a Hodge-like decomposition is applied. The presented theory holds equally well for all types of waves traveling within Cartesian and cylindrical guide geometries (the usual Transverse Electric Magnetic, but also Transverse Magnetic and Transverse Electric ones). We then demonstrate how a generic load decomposes into a series of complex coefficients Zload(α), for each mode α propagating along the line. This decomposition leads to a particular classification of traveling waves: gradient-type and curl-type charge-currents. This distinction shines a new light on a broken gauge symmetry exhibited by a class of Transverse Electric modes. Our results provide a universal theoretical framework, which finds a direct usage in microwave-based quantum information transfer.
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BibTeX
@misc{collin2026quantum,
title = {{Quantum Loads and the Generalized Telegrapher's Problem}},
author = {E. Collin and A. Delattre},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21463},
eprint = {2609.21463},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21463},
}
RIS
TY - UNPB
TI - Quantum Loads and the Generalized Telegrapher's Problem
AU - E. Collin
AU - A. Delattre
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21463
UR - https://arxiv.org/abs/2609.21463
AB - We report on the mapping of classical microwave transmission line theory onto the quantum scattering matrix description. By means of a generalized flux formalism a la Devoret, we derive a charge-current vector living on the confining electrodes, to which a Hodge-like decomposition is applied. The presented theory holds equally well for all types of waves traveling within Cartesian and cylindrical guide geometries (the usual Transverse Electric Magnetic, but also Transverse Magnetic and Transverse Electric ones). We then demonstrate how a generic load decomposes into a series of complex coefficients Z_load(α), for each mode α propagating along the line. This decomposition leads to a particular classification of traveling waves: gradient-type and curl-type charge-currents. This distinction shines a new light on a broken gauge symmetry exhibited by a class of Transverse Electric modes. Our results provide a universal theoretical framework, which finds a direct usage in microwave-based quantum information transfer.
ER -