Exact Virtual Channel Programming with Vanishing Excess Overhead
Abstract
A finite-dimensional physical processor cannot exactly program a continuous family of distinct unitary channels. We show that this obstruction becomes quantitative when the target channel is stored in a normalized Choi state and its output observables are reconstructed by sampling physical channels and classically post-processing their measurement outcomes. For arbitrary d-dimensional channels, we construct a target-independent exact reconstruction protocol and prove the optimal one-copy sampling overhead, which grows quadratically with system dimension. We further prove the sharp fixed-d law that the excess overhead vanishes inversely with the number of identical Choi programs. The upper bound combines deterministic port-based teleportation with a quasi-decomposition that corrects its depolarizing distortion. The converse maps any low-overhead reconstruction protocol to a physical learner of unknown unitaries and uses local quantum estimation to recover the same leading coefficient. These results recast the universal no-programming obstruction as a quantitative trade-off between quantum program memory and classical sampling, with a leading cost that reflects the locally learnable unitary degrees of freedom.
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BibTeX
@misc{jing2026exact,
title = {{Exact Virtual Channel Programming with Vanishing Excess Overhead}},
author = {Mingrui Jing and Mengbo Guo and Hongshun Yao and Xin Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01419},
eprint = {2609.01419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01419},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Virtual Channel Programming with Vanishing Excess Overhead
AU - Mingrui Jing
AU - Mengbo Guo
AU - Hongshun Yao
AU - Xin Wang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01419
UR - https://arxiv.org/abs/2609.01419
AB - A finite-dimensional physical processor cannot exactly program a continuous family of distinct unitary channels. We show that this obstruction becomes quantitative when the target channel is stored in a normalized Choi state and its output observables are reconstructed by sampling physical channels and classically post-processing their measurement outcomes. For arbitrary d-dimensional channels, we construct a target-independent exact reconstruction protocol and prove the optimal one-copy sampling overhead, which grows quadratically with system dimension. We further prove the sharp fixed-d law that the excess overhead vanishes inversely with the number of identical Choi programs. The upper bound combines deterministic port-based teleportation with a quasi-decomposition that corrects its depolarizing distortion. The converse maps any low-overhead reconstruction protocol to a physical learner of unknown unitaries and uses local quantum estimation to recover the same leading coefficient. These results recast the universal no-programming obstruction as a quantitative trade-off between quantum program memory and classical sampling, with a leading cost that reflects the locally learnable unitary degrees of freedom.
ER -