Explicit channels with unbounded gains in classical communication using entangled inputs
Abstract
A seminal result of Hastings showed that entangled inputs can increase the rate of classical communication through independent uses of a quantum channel. While Hastings' result proved the existence of this phenomenon, it has remained a major open problem to find an explicit channel with this property. In this work, we resolve this question by constructing an explicit family of finite-dimensional quantum channels for which entangling inputs between pairs of channel uses yields an unbounded separation from the achievable communication rate using unentangled inputs. We describe a circuit implementation of our channel that uses only deterministic qudit Clifford unitaries and a single binary measurement with classical feedforward. The key ingredient is a careful design of the measurement and feedforward process that yields the required one-copy and two-copy output entropy bounds from moment estimates alone, without requiring strong convergence of the underlying unitary family.
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BibTeX
@misc{cheng2026explicit,
title = {{Explicit channels with unbounded gains in classical communication using entangled inputs}},
author = {Hao-Chung Cheng and Benjamin Lovitz and Peixue Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.26743},
eprint = {2609.26743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26743},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explicit channels with unbounded gains in classical communication using entangled inputs
AU - Hao-Chung Cheng
AU - Benjamin Lovitz
AU - Peixue Wu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.26743
UR - https://arxiv.org/abs/2609.26743
AB - A seminal result of Hastings showed that entangled inputs can increase the rate of classical communication through independent uses of a quantum channel. While Hastings' result proved the existence of this phenomenon, it has remained a major open problem to find an explicit channel with this property. In this work, we resolve this question by constructing an explicit family of finite-dimensional quantum channels for which entangling inputs between pairs of channel uses yields an unbounded separation from the achievable communication rate using unentangled inputs. We describe a circuit implementation of our channel that uses only deterministic qudit Clifford unitaries and a single binary measurement with classical feedforward. The key ingredient is a careful design of the measurement and feedforward process that yields the required one-copy and two-copy output entropy bounds from moment estimates alone, without requiring strong convergence of the underlying unitary family.
ER -