Exact Virtual Channel Programming with Vanishing Excess Overhead

• URL: http://arxiv.org/abs/2609.01419v1
• Date: Tue, 01 Sep 2026 15:35:16 GMT
• Title: Exact Virtual Channel Programming with Vanishing Excess Overhead
• Abstract summary: A finite-dimensional physical processor cannot exactly program a continuous family of distinct unitary channels.<n>We show that this obstruction becomes quantitative when the target channel is stored in a normalized Choi state.<n>For arbitrary $d$-dimensional channels, we construct a target-independent exact reconstruction protocol.
• Score: 4.909277520835048
• License: http://creativecommons.org/licenses/by/4.0/
• 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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