Classical Commitment over Quantum Channels with Limited Entanglement Assistance
Abstract
We study classical string commitment over quantum channels with limited preshared entanglement. For noninteractive protocols, we determine the commitment capacity of a class of channels with input dimension d that, at each use, sample a pair of classical random variables (F,Z), apply one of the d2 Heisenberg--Weyl operators indexed by Z to the input, and deliver the transformed quantum system together with F to the receiver. If E is the available entanglement rate in bits per channel use, then the capacity is min{H(Z|F),log2d+E}. This class of channels encompasses quantum erasure and depolarizing channels, as well as families of Pauli channels. Additionally, for interactive protocols, we show that the commitment rate cannot exceed log2d+E bits per channel use, so that when H(Z|F)≥log2d+E, interactive communication does not increase the capacity. As a consequence, for interactive protocols, we determine the capacity of the quantum erasure channel.
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BibTeX
@misc{chou2026classical,
title = {{Classical Commitment over Quantum Channels with Limited Entanglement Assistance}},
author = {Remi A. Chou},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28500},
eprint = {2608.28500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28500},
}
RIS
TY - UNPB
TI - Classical Commitment over Quantum Channels with Limited Entanglement Assistance
AU - Remi A. Chou
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28500
UR - https://arxiv.org/abs/2608.28500
AB - We study classical string commitment over quantum channels with limited preshared entanglement. For noninteractive protocols, we determine the commitment capacity of a class of channels with input dimension d that, at each use, sample a pair of classical random variables (F,Z), apply one of the d^2 Heisenberg--Weyl operators indexed by Z to the input, and deliver the transformed quantum system together with F to the receiver. If E is the available entanglement rate in bits per channel use, then the capacity is min{H(Z|F),log_2d+E}. This class of channels encompasses quantum erasure and depolarizing channels, as well as families of Pauli channels. Additionally, for interactive protocols, we show that the commitment rate cannot exceed log_2d+E bits per channel use, so that when H(Z|F)≥log_2d+E, interactive communication does not increase the capacity. As a consequence, for interactive protocols, we determine the capacity of the quantum erasure channel.
ER -