Flux-Based Time Bounds for Harmonically Degenerate Quantum Systems
Abstract
We study transfer-time estimates for finite-dimensional bilinear quantum control systems driven by an unbounded scalar control, in both the state-to-state setting (complex projective space) and the unitary synthesis setting (special unitary group). Lower bounds are recalled and refined via spectral and chordal methods. The main contribution is constructive upper bounds: we associate with the system a coupling graph whose edges correspond to non-resonant drift couplings, and construct transfer protocols along spanning trees. In contrast with earlier results requiring full rational independence of the spectrum of the control operator, our estimates allow rational resonances; they incorporate, via explicit correction factors derived from the arithmetic of the spectral gaps, the efficiency of the averaging procedure and of the phase adjustments. As an application, we consider finite-dimensional truncations of the planar quantum rotator under a dipolar electric field, and show that the transfer time between any two modes tends to zero as the truncation dimension grows.
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BibTeX
@misc{chambrion2026fluxbased,
title = {{Flux-Based Time Bounds for Harmonically Degenerate Quantum Systems}},
author = {Thomas Chambrion},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26205},
eprint = {2610.26205},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05803694v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Flux-Based Time Bounds for Harmonically Degenerate Quantum Systems
AU - Thomas Chambrion
PY - 2026
DA - 2026/10/16
PB - HAL
DO - 10.48550/arxiv.2610.26205
UR - https://hal.science/hal-05803694v1
AB - We study transfer-time estimates for finite-dimensional bilinear quantum control systems driven by an unbounded scalar control, in both the state-to-state setting (complex projective space) and the unitary synthesis setting (special unitary group). Lower bounds are recalled and refined via spectral and chordal methods. The main contribution is constructive upper bounds: we associate with the system a coupling graph whose edges correspond to non-resonant drift couplings, and construct transfer protocols along spanning trees. In contrast with earlier results requiring full rational independence of the spectrum of the control operator, our estimates allow rational resonances; they incorporate, via explicit correction factors derived from the arithmetic of the spectral gaps, the efficiency of the averaging procedure and of the phase adjustments. As an application, we consider finite-dimensional truncations of the planar quantum rotator under a dipolar electric field, and show that the transfer time between any two modes tends to zero as the truncation dimension grows.
ER -